This project investigates mathematical psychology's historical and philosophical foundations to clarify its distinguishing characteristics and relationships to adjacent fields. Through gathering primary sources, histories, and interviews with researchers, author Prof. Colin Allen - University of Pittsburgh [1, 2, 3] and his students Osman Attah, Brendan Fleig-Goldstein, Mara McGuire, and Dzintra Ullis have identified three central questions:
What makes the use of mathematics in mathematical psychology reasonably effective, in contrast to other sciences like physics-inspired mathematical biology or symbolic cognitive science? How does the mathematical approach in mathematical psychology differ from other branches of psychology, like psychophysics and psychometrics? What is the appropriate relationship of mathematical psychology to cognitive science, given diverging perspectives on aligning with this field?
Preliminary findings emphasize data-driven modeling, skepticism of cognitive science alignments, and early reliance on computation. They will further probe the interplay with cognitive neuroscience and contrast rational-analysis approaches. By elucidating the motivating perspectives and objectives of different eras in mathematical psychology's development, they aim to understand its past and inform constructive dialogue on its philosophical foundations and future directions. This project intends to provide a conceptual roadmap for the field through integrated history and philosophy of science.
The Project: Integrating History and Philosophy of Mathematical Psychology
This project aims to integrate historical and philosophical perspectives to elucidate the foundations of mathematical psychology. As Norwood Hanson stated, history without philosophy is blind, while philosophy without history is empty. The goal is to find a middle ground between the contextual focus of history and the conceptual focus of philosophy.
The team acknowledges that all historical accounts are imperfect, but some can provide valuable insights. The history of mathematical psychology is difficult to tell without centering on the influential Stanford group. Tracing academic lineages and key events includes part of the picture, but more context is needed to fully understand the field's development.
The project draws on diverse sources, including research interviews, retrospective articles, formal histories, and online materials. More interviews and research will further flesh out the historical and philosophical foundations. While incomplete, the current analysis aims to identify important themes, contrasts, and questions that shaped mathematical psychology's evolution. Ultimately, the goal is an integrated historical and conceptual roadmap to inform contemporary perspectives on the field's identity and future directions.
The Rise of Mathematical Psychology
The history of efforts to mathematize psychology traces back to the quantitative imperative stemming from the Galilean scientific revolution. This imprinted the notion that proper science requires mathematics, leading to "physics envy" in other disciplines like psychology.
Many early psychologists argued psychology needed to become mathematical to be scientific. However, mathematizing psychology faced complications absent in the physical sciences. Objects in psychology were not readily present as quantifiable, provoking heated debates on whether psychometric and psychophysical measurements were meaningful.
Nonetheless, the desire to develop mathematical psychology persisted. Different approaches grappled with determining the appropriate role of mathematics in relation to psychological experiments and data. For example, Herbart favored starting with mathematics to ensure accuracy, while Fechner insisted experiments must come first to ground mathematics.
Tensions remain between data-driven versus theory-driven mathematization of psychology. Contemporary perspectives range from psychometric and psychophysical stances that foreground data to measurement-theoretical and computational approaches that emphasize formal models.
Elucidating how psychologists negotiated to apply mathematical methods to an apparently resistant subject matter helps reveal the evolving role and place of mathematics in psychology. This historical interplay shaped the emergence of mathematical psychology as a field.
The Distinctive Mathematical Approach of Mathematical Psychology
What sets mathematical psychology apart from other branches of psychology in its use of mathematics?
Several key aspects stand out:
Advocating quantitative methods broadly. Mathematical psychology emerged partly to push psychology to embrace quantitative modeling and mathematics beyond basic statistics. Drawing from diverse mathematical tools. With greater training in mathematics, mathematical psychologists utilize more advanced and varied mathematical techniques like topology and differential geometry. Linking models and experiments. Mathematical psychologists emphasize tightly connecting experimental design and statistical analysis, with experiments created to test specific models. Favoring theoretical models. Mathematical psychology incorporates "pure" mathematical results and prefers analytic, hand-fitted models over data-driven computer models. Seeking general, cumulative theory. Unlike just describing data, mathematical psychology aspires to abstract, general theory supported across experiments, cumulative progress in models, and mathematical insight into psychological mechanisms.
So while not unique to mathematical psychology, these key elements help characterize how its use of mathematics diverges from adjacent fields like psychophysics and psychometrics. Mathematical psychology carved out an identity embracing quantitative methods but also theoretical depth and broad generalization.
Situating Mathematical Psychology Relative to Cognitive Science
What is the appropriate perspective on mathematical psychology's relationship to cognitive psychology and cognitive science? While connected historically and conceptually, essential distinctions exist.
Mathematical psychology draws from diverse disciplines that are also influential in cognitive science, like computer science, psychology, linguistics, and neuroscience. However, mathematical psychology appears more skeptical of alignments with cognitive science.
For example, cognitive science prominently adopted the computer as a model of the human mind, while mathematical psychology focused more narrowly on computers as modeling tools.
Additionally, mathematical psychology seems to take a more critical stance towards purely simulation-based modeling in cognitive science, instead emphasizing iterative modeling tightly linked to experimentation.
Overall, mathematical psychology exhibits significant overlap with cognitive science but strongly asserts its distinct mathematical orientation and modeling perspectives. Elucidating this complex relationship remains an ongoing project, but preliminary analysis suggests mathematical psychology intentionally diverged from cognitive science in its formative development.
This establishes mathematical psychology's separate identity while retaining connections to adjacent disciplines at the intersection of mathematics, psychology, and computation.
Looking Ahead: Open Questions and Future Research
This historical and conceptual analysis of mathematical psychology's foundations has illuminated key themes, contrasts, and questions that shaped the field's development. Further research can build on these preliminary findings.
Additional work is needed to flesh out the fuller intellectual, social, and political context driving the evolution of mathematical psychology. Examining the influences and reactions of key figures will provide a richer picture.
Ongoing investigation can probe whether the identified tensions and contrasts represent historical artifacts or still animate contemporary debates. Do mathematical psychologists today grapple with similar questions on the role of mathematics and modeling?
Further analysis should also elucidate the nature of the purported bidirectional relationship between modeling and experimentation in mathematical psychology. As well, clarifying the diversity of perspectives on goals like generality, abstraction, and cumulative theory-building would be valuable.
Finally, this research aims to spur discussion on philosophical issues such as realism, pluralism, and progress in mathematical psychology models. Is the accuracy and truth value of models an important consideration or mainly beside the point? And where is the field headed - towards greater verisimilitude or an indefinite balancing of complexity and abstraction?
By spurring reflection on this conceptual foundation, this historical and integrative analysis hopes to provide a roadmap to inform constructive dialogue on mathematical psychology's identity and future trajectory.
The SDTEST®
The SDTEST® is a simple and fun tool to uncover our unique motivational values that use mathematical psychology of varying complexity.
VIDEO
The SDTEST® helps us better understand ourselves and others on this lifelong path of self-discovery.
Here are reports of polls which SDTEST® makes:
1) පසුගිය මාසයේ පිරිස් සම්බන්ධ සමාගම්වල ක්රියා (ඔව් / නැත)
2) පසුගිය මාසයේ පිරිස් සම්බන්ධ සමාගම්වල ක්රියා (සත්යය%)
3) බිය
4) මගේ රට මුහුණ දෙන විශාලතම ගැටළු
5) සාර්ථක කණ්ඩායම් තැනීමේදී හොඳ නායකයින් භාවිතා කරන ගුණාංග හා හැකියාවන් මොනවාද?
6) ගූගල්. කණ්ඩායම් විනාශකාරීත්වයට බලපාන සාධක
7) රැකියා අපේක්ෂකයින්ගේ ප්රධාන ප්රමුඛතා
8) ලොක්කා විශිෂ්ට නායකයෙකු වන්නේ කුමක් ද?
9) රැකියාවෙහි මිනිසුන් සාර්ථක වීමට හේතුව කුමක්ද?
10) දුරස්ථව වැඩ කිරීම සඳහා අඩු වැටුපක් ලබා ගැනීමට ඔබ සූදානම්ද?
11) වයස්වාදය පවතින්නේද?
12) වෘත්තියේ වෘත්තිය
13) ජීවිතයේ වයස
14) වයස්වාදයේ හේතු
15) මිනිසුන් අත්හරින විට (ඇනා අත්යවශ්ය)
16) විශ්වාසය (#WVS)
17) ඔක්ස්ෆර්ඩ් සතුට සමීක්ෂණය
18) මනෝවිද්යාත්මක යහපැවැත්ම
19) ඔබගේ ඊළඟ ආකර්ෂණීය අවස්ථාව කොහිද?
20) ඔබේ මානසික සෞඛ්යය ගැන සොයා බැලීමට ඔබ මේ සතියේ කරන්නේ කුමක්ද?
21) මම ජීවත් වන්නේ මගේ අතීතය, වර්තමාන හෝ අනාගතය ගැන සිතීමයි
22) රසකාරක
23) කෘතිම බුද්ධිය සහ ශිෂ්ටාචාරයේ අවසානය
24) මිනිසුන් කල් දමන්නේ ඇයි?
25) ආත්ම විශ්වාසය ගොඩනැගීමේ ස්ත්රී පුරුෂ වෙනස (අයිඑෆ්ඩී ඇලස්බැක්)
26) Xing.com සංස්කෘතික තක්සේරුව
27) පැට්රික් ලෙන්කෝනිගේ "කණ්ඩායමක අක්රිය පහක්"
28) සංවේදනය ...
29) රැකියා දීමනාවක් තෝරා ගැනීමේදී තොරතුරු තාක්ෂණ විශේෂ ists යින්ට අත්යවශ්ය වන්නේ කුමක්ද?
30) මිනිසුන් වෙනස් වීමට විරුද්ධ වන්නේ ඇයි (SIOBHHán Mchale විසින්)
31) ඔබ ඔබේ හැඟීම් නියාමනය කරන්නේ කෙසේද? (නවාල් මුස්තාපා m.a.)
32) සදහටම ඔබට ගෙවන කුසලතා 21 ක් (ජෙරමියා තේ / 赵汉昇 විසිනි)
33) සැබෑ නිදහස ...
34) අන් අය සමඟ විශ්වාසය ගොඩනඟා ගැනීමට ක්රම 12 ක් (ජස්ටින් රයිට් විසින්)
35) දක්ෂ සේවකයෙකුගේ ලක්ෂණ (කුසලතා කළමනාකරණ ආයතනය අනුව)
36) ඔබේ කණ්ඩායම පෙළඹවීම සඳහා යතුරු 10 ක්
37) හෘද සාක්ෂියේ වීජ ගණිතය (Vladimir Lefebvre විසිනි)
38) අනාගතයේ වෙනස් අවස්ථා තුනක් (Dr. Clare W. Graves විසිනි)
39) නොසැලෙන ආත්ම විශ්වාසය ගොඩනැගීමට ක්රියා (සුරේන් සමර්ච්යන් විසිනි)
40)
Below you can read an abridged version of the results of our VUCA poll “Fears“ . The full version of the results is available for free in the FAQ section after login or registration .
බිය
ප්රස්ථාර සහසම්බන්ධ
?
VUCA
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සියලුම ප්රශ්න
මගේ ලොකුම බිය
මගේ ලොකුම බිය
Answer 1
11%
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5
5
5
5
4
5
5
1
5
0
2
4
0
5
5
5
3
3
4
5
1
2
5
4
3
3
5
5
0
5
0
5
4
4
5
3
1
4
0
5
3
5
5
4
5
0
0
5
3
5
5
3
1
5
0
5
0
4
5
4
1
1
5
5
2
5
3
3
5
5
2
0
0
5
2
2
0
4
5
5
4
4
2
5
5
0
0
4
5
4
5
5
3
4
5
0
2
0
0
5
5
0
5
0
0
4
5
0
3
4
0
4
5
5
5
4
4
4
1
1
4
4
3
2
5
5
4
5
0
5
4
3
5
5
3
5
5
3
3
0
4
5
4
1
5
5
1
3
1
0
3
3
4
5
0
4
5
1
1
5
0
5
0
5
5
5
5
1
5
5
5
0
5
5
2
5
4
5
2
3
5
0
5
5
5
4
0
4
0
5
1
3
5
5
5
2
4
5
4
0
5
5
2
5
5
3
4
5
0
1
3
3
1
5
5
0
0
5
2
0
5
0
5
5
2
4
5
5
5
4
3
4
0
5
5
3
5
5
1
4
3
5
3
5
5
0
5
5
5
2
5
5
5
5
1
5
4
4
5
0
0
2
5
5
0
0
0
5
5
5
5
5
5
5
5
4
5
5
5
5
5
0
5
5
4
5
0
5
3
2
5
5
3
5
4
4
0
1
5
5
5
5
5
5
5
3
5
5
3
2
5
1
0
4
5
4
5
5
0
1
1
2
5
2
5
0
5
1
3
5
5
0
4
5
4
5
2
5
4
5
3
0
3
2
3
5
2
3
5
3
3
3
0
2
0
5
5
5
0
3
0
5
5
5
0
1
5
2
0
3
3
5
5
5
0
4
5
3
5
5
5
4
5
5
3
1
5
5
5
5
5
5
3
5
2
2
5
5
5
3
4
5
1
4
4
4
2
0
2
3
4
0
4
5
0
1
4
4
0
0
5
0
5
0
5
5
5
3
5
4
1
0
3
2
5
5
5
5
0
Answer 2
8%
0
0
5
0
5
4
3
2
1
0
3
5
0
5
4
5
0
1
4
5
3
0
1
3
0
2
5
5
3
5
0
1
0
3
4
3
2
0
5
5
5
0
3
3
1
4
0
4
1
0
0
0
2
5
2
5
2
4
5
5
0
5
5
1
4
5
5
0
1
0
4
5
4
5
0
5
2
0
4
3
3
3
5
3
4
4
3
4
4
5
5
0
3
0
0
4
2
0
3
5
3
1
1
0
5
4
0
5
5
4
0
0
5
4
4
2
0
0
4
5
4
2
1
0
3
3
3
1
2
1
0
2
4
0
2
0
0
0
2
3
2
5
2
0
1
5
0
4
0
0
2
4
5
4
5
4
3
0
0
5
1
0
5
1
3
2
1
0
3
0
2
5
0
0
2
0
4
5
0
1
5
3
0
5
1
5
2
0
0
0
5
5
0
1
1
5
1
3
2
3
1
1
4
4
5
4
1
0
3
0
1
2
4
2
5
5
0
0
0
0
0
0
0
2
1
3
3
0
0
0
4
1
3
0
3
1
1
5
1
0
5
3
5
0
5
3
5
5
3
3
0
0
0
5
0
0
0
5
0
0
0
0
1
5
5
3
0
1
5
1
2
5
2
0
4
5
2
4
0
0
5
2
3
2
0
5
3
0
2
0
0
3
0
5
0
4
4
3
4
0
2
5
4
3
5
1
0
0
5
2
0
4
2
1
5
0
0
3
1
3
0
1
3
1
0
2
3
4
0
0
5
5
0
4
3
3
3
2
3
5
5
1
2
1
0
5
5
3
0
4
0
5
1
3
5
3
3
2
5
5
3
4
3
5
1
5
5
3
2
5
4
3
0
0
5
0
5
0
4
2
1
5
0
0
1
5
0
0
5
1
1
1
2
5
3
0
2
2
1
1
5
3
0
5
1
0
3
0
1
2
0
1
2
0
2
1
3
2
0
1
4
0
5
3
4
0
0
4
4
5
0
3
2
1
4
0
5
5
3
1
3
3
5
2
0
5
5
2
1
0
0
3
5
0
5
5
2
4
0
2
0
2
2
3
0
1
3
4
1
2
0
2
0
3
2
0
0
2
3
0
0
5
0
2
4
5
5
4
4
2
3
2
0
1
0
0
3
1
0
2
3
0
5
5
1
0
5
1
2
3
0
2
5
5
2
0
4
3
4
5
5
0
0
5
0
4
2
3
4
4
2
0
0
0
3
3
5
4
0
5
4
5
3
3
3
1
4
1
4
1
0
0
0
4
4
2
5
1
2
5
5
0
5
0
0
5
0
5
5
0
1
0
5
3
0
0
5
0
1
4
4
0
0
0
0
0
0
5
5
0
0
5
3
1
2
5
0
1
4
5
0
5
2
1
4
5
2
5
5
5
5
0
3
5
5
5
1
2
1
5
4
5
3
1
5
3
2
1
5
1
0
0
5
4
2
0
1
1
0
0
3
0
2
0
2
3
0
3
5
2
1
1
3
3
2
5
3
4
3
4
3
1
0
4
3
2
5
0
1
5
1
2
4
1
4
2
0
2
4
2
2
0
2
4
2
1
3
5
3
4
1
1
3
3
4
3
5
0
1
3
3
0
4
2
2
5
0
3
4
5
4
1
1
5
0
3
2
5
1
2
5
5
0
3
4
5
3
2
1
4
3
3
0
1
4
0
4
0
3
0
3
3
1
4
4
5
0
1
5
5
3
5
4
0
5
1
2
0
1
5
5
5
4
1
0
0
1
5
1
0
5
2
5
1
5
3
2
3
0
5
2
2
1
3
4
0
0
3
0
3
1
1
5
0
2
4
0
0
0
4
2
1
5
2
5
1
4
5
0
4
0
0
1
4
1
0
0
5
0
5
2
4
0
1
3
1
1
3
4
0
1
4
4
4
5
2
0
0
1
0
3
4
5
0
5
2
5
0
0
1
4
5
5
4
5
3
5
0
5
0
3
0
0
4
3
5
5
0
3
3
3
4
0
2
2
5
5
5
3
3
0
3
5
4
0
5
0
0
4
5
3
5
2
1
2
3
4
5
5
3
0
5
5
5
5
0
3
4
1
2
0
1
5
0
2
5
1
2
2
2
3
4
0
0
2
4
0
5
2
3
3
5
0
3
4
0
1
3
0
5
0
0
2
3
0
0
5
3
0
3
0
4
5
2
0
4
5
3
4
0
5
0
4
1
0
1
4
1
1
3
2
0
1
4
0
5
0
4
4
0
2
2
1
0
0
0
4
4
4
5
1
5
0
0
0
2
1
2
3
2
5
1
2
0
3
3
0
3
0
2
4
0
5
0
5
4
3
2
1
0
3
0
5
5
2
1
0
4
5
2
2
4
5
3
5
3
1
4
1
0
1
0
0
3
0
5
2
5
4
1
4
3
0
3
3
0
0
4
4
3
2
4
0
5
1
1
0
4
5
0
2
3
0
2
3
2
5
4
0
0
0
0
0
0
0
3
4
5
3
4
2
0
0
5
3
0
1
0
3
1
0
5
2
0
0
0
0
4
0
0
0
4
5
1
5
0
0
1
1
0
4
1
2
3
0
0
4
4
1
0
0
4
0
5
3
0
2
5
5
0
4
3
2
3
5
5
4
5
3
0
0
3
4
1
2
3
3
3
5
3
0
2
0
0
4
2
0
0
1
0
1
0
0
3
5
2
3
4
1
1
2
1
3
1
5
5
3
0
3
5
5
2
0
4
2
5
5
2
5
2
0
0
2
1
0
3
2
5
5
3
1
5
1
0
5
1
1
0
5
0
3
1
5
0
2
1
2
5
3
5
2
3
5
1
0
3
2
3
5
1
5
5
3
3
2
4
4
0
0
3
2
1
0
3
4
4
0
0
5
3
3
0
2
0
0
4
2
5
2
4
4
5
4
0
4
4
5
5
5
0
4
2
0
0
5
4
5
3
4
0
5
5
2
4
1
0
3
4
5
2
2
2
2
1
1
5
2
0
4
5
2
3
4
4
3
4
3
0
5
5
5
4
1
2
5
3
4
1
5
5
0
3
0
3
1
4
0
0
0
5
4
1
3
3
4
0
5
5
0
5
4
1
5
0
3
0
1
3
0
0
2
5
5
3
3
5
5
0
4
0
4
0
5
0
5
0
2
5
5
0
5
4
0
3
0
0
1
0
2
0
2
4
0
3
2
0
4
4
3
1
4
2
0
0
3
2
3
3
5
3
3
4
5
5
0
3
2
3
5
5
3
2
0
1
5
2
3
4
3
3
4
0
3
3
1
1
3
2
3
0
4
3
0
0
0
0
0
1
0
5
0
4
1
3
3
5
5
0
5
0
3
3
2
0
5
3
0
5
3
4
4
1
1
5
0
1
5
0
2
0
0
0
4
1
5
5
1
0
5
0
5
5
0
2
5
4
2
1
5
5
3
3
5
1
5
5
0
5
1
4
3
4
5
0
4
0
2
2
0
0
3
4
0
1
3
0
2
2
2
3
1
0
3
5
3
4
4
0
0
4
4
1
5
1
2
3
0
4
1
4
2
0
3
3
4
0
5
1
0
2
3
2
1
0
4
1
0
4
4
1
3
0
3
0
2
4
5
5
2
4
1
5
5
1
2
5
2
0
0
0
1
0
0
3
0
3
4
2
3
5
3
5
1
2
2
1
4
1
5
0
3
5
5
2
5
1
5
2
4
3
0
0
4
1
2
5
0
2
5
1
0
0
1
0
1
1
0
1
0
0
1
2
0
5
1
3
3
2
3
2
2
1
4
0
5
4
4
0
0
0
3
0
5
1
0
0
3
1
3
0
1
0
3
2
3
2
5
1
1
4
0
5
3
0
5
2
5
5
1
1
3
5
0
4
2
4
5
3
1
4
1
4
0
2
0
1
5
5
4
5
4
5
0
0
0
5
3
3
3
4
4
0
0
3
3
0
1
0
0
0
3
5
0
0
5
2
0
3
2
1
3
5
5
5
2
1
5
0
5
0
5
4
5
0
1
0
0
0
0
4
1
2
4
0
3
5
4
2
2
3
0
0
4
3
4
2
5
5
3
5
5
5
0
3
2
4
3
3
2
5
1
2
0
5
5
3
0
0
0
1
2
0
2
4
5
0
3
0
2
0
2
0
4
0
1
3
5
4
3
1
1
0
0
3
3
5
0
0
0
0
2
0
0
3
1
2
0
2
0
2
4
3
3
3
3
2
5
5
2
1
0
2
0
2
3
3
3
0
3
3
0
1
3
2
2
2
4
4
2
0
0
1
0
5
1
2
4
2
1
1
2
3
0
3
4
5
4
3
4
3
2
3
5
0
4
4
3
0
5
1
1
4
3
5
5
0
0
0
5
1
0
3
5
4
0
0
5
5
0
1
0
3
3
0
0
3
0
1
3
5
1
5
2
0
1
1
3
0
3
5
5
1
4
5
0
0
2
0
1
5
0
5
0
3
4
1
0
0
1
3
5
5
3
0
0
4
5
4
5
0
0
4
0
5
1
0
2
1
5
0
1
0
5
3
0
0
0
1
0
0
0
4
3
3
3
3
2
0
0
5
5
1
5
0
3
0
5
2
4
3
4
3
1
5
0
3
5
5
5
0
4
3
0
1
3
5
5
4
5
0
1
5
5
0
1
3
1
0
3
5
4
1
1
5
5
4
0
2
0
3
1
5
0
4
0
5
5
4
0
0
4
5
0
3
3
4
0
3
4
0
4
5
0
0
5
5
1
2
2
0
2
1
0
3
0
1
0
1
4
0
5
0
5
4
0
5
4
2
4
1
3
3
0
0
2
1
1
4
3
5
4
5
1
5
0
2
0
2
3
4
3
5
5
3
4
1
0
0
0
2
3
3
2
0
0
1
0
2
3
5
2
5
5
5
0
0
4
1
3
0
5
3
4
1
0
0
5
5
0
1
3
0
1
3
0
2
4
4
5
2
3
3
1
1
3
5
3
4
5
0
3
1
5
0
2
2
0
0
5
5
5
0
0
0
0
4
1
0
0
2
2
0
2
0
2
0
4
2
3
2
0
3
2
1
5
2
5
2
3
5
0
2
3
5
5
3
0
2
3
2
3
2
3
1
2
0
0
0
4
3
3
0
5
0
0
4
2
5
1
0
3
5
0
4
3
0
4
1
4
2
5
2
4
3
5
4
5
0
2
5
5
3
2
5
3
0
1
1
5
1
5
0
0
3
3
4
2
2
5
0
0
5
3
3
0
5
2
5
5
5
5
2
0
5
4
5
1
5
3
5
0
1
3
0
3
5
1
0
3
0
5
0
2
0
2
0
0
3
4
0
0
5
0
1
4
3
3
4
5
0
4
4
3
4
4
5
4
5
5
4
5
5
4
5
5
4
2
5
5
3
0
2
2
2
4
5
3
3
1
4
3
5
2
0
5
3
0
5
2
2
5
5
4
0
3
3
2
1
0
0
4
5
0
1
3
5
4
0
3
3
5
0
3
5
5
4
2
5
4
0
5
1
1
0
3
0
3
0
4
2
5
0
0
4
1
0
4
2
2
3
0
3
5
5
5
2
0
3
2
5
1
3
5
1
4
5
4
2
0
5
3
5
1
1
4
4
5
0
4
3
0
5
5
5
0
0
2
5
5
0
3
4
0
2
1
2
3
2
5
0
1
1
0
0
1
0
3
4
5
2
4
2
5
4
3
3
0
5
1
5
0
5
0
1
3
2
5
3
2
3
1
5
4
5
5
5
1
2
1
4
4
1
5
0
3
5
5
0
2
3
5
0
2
5
4
2
5
2
5
1
0
5
3
1
1
0
3
2
0
0
1
5
4
3
5
3
2
3
2
5
1
4
5
2
5
5
4
0
3
1
5
0
3
0
4
3
0
2
2
0
4
0
1
2
1
3
0
1
0
5
1
4
5
4
3
0
1
0
0
5
5
4
4
0
3
0
0
5
5
5
0
4
4
3
5
5
5
0
1
3
0
5
3
2
5
1
2
4
0
5
5
5
3
5
0
0
3
0
2
5
0
5
5
1
4
3
5
5
5
0
1
5
2
3
5
1
0
0
1
0
3
0
4
3
5
5
5
0
5
4
3
0
0
5
3
5
5
1
5
5
0
0
2
0
5
0
4
0
4
3
4
0
2
2
2
4
0
2
1
3
0
5
0
0
0
3
5
3
0
1
0
0
0
2
3
0
4
3
5
0
3
5
3
3
1
5
0
0
5
5
3
4
3
5
5
1
2
0
5
0
0
2
3
0
0
2
2
3
3
0
4
5
0
0
1
4
5
2
0
0
0
1
2
2
2
4
0
0
0
2
0
2
0
0
5
0
0
5
5
3
5
1
3
0
0
3
4
3
5
0
5
5
5
3
5
3
2
5
3
3
5
1
4
1
0
2
3
3
3
4
5
5
4
0
3
1
2
3
0
0
3
0
3
4
3
4
1
5
4
0
0
2
4
2
1
3
5
2
2
1
5
5
1
3
0
3
3
0
0
5
0
1
1
5
0
1
5
0
3
3
4
0
0
1
5
2
0
1
0
1
5
0
0
3
1
4
0
0
3
5
3
1
0
4
1
3
5
5
2
3
5
1
4
0
4
0
2
3
3
3
0
2
2
3
1
4
0
0
0
5
1
0
1
1
4
5
1
5
0
0
4
5
3
2
3
1
5
4
5
5
0
1
4
0
0
0
2
0
0
0
4
4
2
2
4
5
5
1
1
5
0
0
5
3
2
3
2
0
0
1
5
0
5
5
0
5
5
2
0
2
3
1
5
1
4
1
5
4
5
5
4
1
5
3
4
3
5
0
4
3
5
4
0
1
3
0
0
0
2
0
0
5
2
0
5
5
3
2
0
4
4
1
5
1
1
3
5
5
3
0
0
0
2
0
0
3
3
0
0
0
4
1
0
1
3
2
3
1
0
0
5
4
3
5
3
5
2
0
3
3
4
5
1
0
1
0
5
2
1
4
2
2
1
0
2
0
2
4
0
3
5
0
3
3
0
1
5
1
5
5
5
0
1
3
3
3
4
4
2
2
0
0
4
0
3
5
3
0
0
3
5
3
1
3
2
3
3
2
4
4
1
5
5
5
5
5
2
2
2
2
4
0
0
2
5
0
1
2
5
4
5
4
5
3
1
5
3
0
5
0
4
0
2
3
2
0
1
0
0
2
0
0
4
2
3
3
4
1
1
3
3
0
5
4
5
2
1
2
4
5
0
4
3
3
5
0
3
5
5
5
5
3
0
5
3
2
5
0
0
4
1
2
4
2
4
0
5
2
3
5
5
2
5
1
3
0
1
2
3
5
1
2
3
2
0
4
1
3
4
0
4
0
0
0
1
0
0
0
3
5
4
5
5
5
4
3
2
0
0
5
5
4
5
4
4
2
1
5
4
5
1
0
5
3
4
4
0
0
2
2
5
0
5
5
0
3
2
5
1
5
0
1
2
5
1
3
0
3
5
0
5
2
2
1
1
0
0
1
0
2
2
5
4
0
3
0
4
0
0
3
5
0
0
2
5
5
5
3
0
0
3
0
3
3
0
2
1
2
0
0
0
3
0
5
0
4
0
5
1
5
5
5
1
0
1
4
5
2
2
0
0
3
0
1
2
3
3
0
0
5
5
3
5
0
0
0
2
5
0
0
0
5
3
5
2
1
5
5
0
5
3
2
0
3
5
0
1
0
0
3
1
5
1
1
4
2
3
0
5
0
0
5
3
4
5
0
0
4
3
0
0
3
0
3
2
5
2
3
2
5
5
1
3
0
1
4
4
3
1
2
4
3
0
0
0
0
0
0
3
5
0
0
3
4
1
3
2
3
2
3
3
5
3
0
3
2
0
2
3
3
2
2
5
0
1
0
1
1
0
5
2
4
3
5
3
0
3
0
0
0
2
1
1
5
2
0
5
3
2
0
4
5
4
5
2
4
0
1
0
5
3
2
0
1
5
2
0
4
0
0
0
0
4
0
0
1
4
3
3
5
2
3
0
4
0
4
0
3
0
0
3
0
3
5
0
2
3
0
2
4
2
2
5
2
3
4
3
1
4
3
0
3
0
5
4
1
3
5
0
2
4
5
5
4
3
2
4
2
3
5
0
0
0
3
2
0
4
2
0
1
3
1
3
5
0
3
4
5
5
0
5
0
0
0
3
2
0
2
5
3
2
0
0
5
0
0
5
5
0
5
3
0
4
0
0
5
5
3
4
0
3
2
1
0
5
0
3
0
5
5
2
2
0
5
1
2
3
5
4
3
3
3
2
5
3
5
1
0
4
5
5
2
1
0
0
1
0
1
0
2
2
1
1
4
1
3
0
3
0
0
2
4
2
2
3
5
4
5
2
4
0
4
3
5
4
0
5
1
0
3
0
3
0
5
1
3
4
4
2
4
0
0
0
0
0
3
3
5
4
3
3
1
0
5
4
1
4
5
3
0
0
1
0
3
4
0
1
4
0
0
0
5
0
4
5
5
0
2
0
0
3
4
1
3
3
0
1
3
3
0
4
4
5
0
5
0
4
0
1
5
4
3
3
0
0
3
5
5
0
0
0
5
0
5
5
5
0
5
5
2
5
0
0
4
3
1
4
5
2
5
0
0
2
2
3
3
2
4
4
5
5
1
5
4
5
4
5
0
3
1
3
3
3
0
0
1
3
0
0
5
5
5
4
1
4
4
5
4
3
0
0
1
0
5
2
4
4
3
4
5
1
0
5
4
5
0
2
1
1
5
2
1
2
1
2
3
5
3
0
3
2
3
4
3
0
0
2
4
0
0
0
0
0
0
1
3
0
0
0
2
0
0
5
5
2
3
3
3
0
5
1
5
4
5
0
4
2
5
0
4
0
3
0
5
5
0
3
2
3
5
2
4
3
2
4
0
3
3
4
0
3
0
5
0
1
3
3
3
3
1
0
4
5
0
0
0
2
5
3
2
2
0
0
Answer 3
7%
3
0
0
0
0
0
3
3
1
0
3
0
5
5
5
1
1
0
2
3
3
5
0
1
0
5
3
0
5
0
0
0
0
0
3
2
0
4
3
2
5
0
1
4
1
1
1
4
2
0
0
0
2
2
3
4
5
4
5
5
0
5
0
0
2
0
5
0
0
0
0
0
2
0
0
3
4
1
2
2
2
0
4
0
3
3
0
3
3
1
0
3
3
2
2
0
2
0
4
4
3
2
1
0
4
0
4
3
3
0
0
3
3
2
0
3
0
0
5
4
5
3
0
0
2
5
3
1
2
1
0
0
2
1
2
0
3
0
1
0
2
5
3
0
0
0
0
3
3
0
5
4
2
5
4
5
4
2
0
0
2
4
0
2
1
3
0
0
2
0
3
5
0
0
4
0
2
2
0
1
5
3
5
5
0
2
1
0
0
3
1
4
0
2
3
2
0
1
3
2
3
0
0
4
4
0
2
0
2
0
1
1
2
3
3
4
5
0
4
1
0
0
0
2
3
3
3
0
2
0
5
2
2
1
0
0
1
1
0
0
3
1
5
3
2
5
0
5
4
0
0
0
2
4
0
0
4
5
2
1
0
0
1
0
0
0
0
2
0
2
1
5
1
0
1
4
1
3
0
2
3
3
2
4
0
0
0
0
1
5
0
5
5
4
0
2
2
0
3
0
0
4
3
3
5
3
2
0
4
4
0
1
0
0
5
0
2
2
1
0
0
1
5
0
0
4
0
2
0
3
5
5
3
4
0
2
0
5
4
3
2
3
4
1
3
3
3
1
0
1
0
3
1
3
5
0
2
3
2
5
5
3
2
5
4
3
1
0
1
4
2
0
0
0
5
2
4
0
3
2
1
4
0
4
1
1
0
0
5
2
1
4
4
5
4
1
2
2
5
4
3
4
0
2
0
0
3
0
4
2
2
2
0
0
3
1
1
1
0
1
5
0
3
1
1
0
0
0
5
5
1
2
1
5
0
0
3
0
0
0
3
0
4
2
1
3
0
1
0
0
0
4
4
0
5
2
0
4
1
1
5
2
5
3
0
1
0
4
3
5
0
3
0
1
0
5
0
3
0
0
5
5
0
3
3
5
0
0
1
0
0
1
0
1
3
0
0
1
2
0
5
5
2
2
5
0
3
4
3
4
2
2
4
5
1
0
0
3
5
1
0
0
3
5
3
3
5
5
3
3
3
0
0
5
0
0
4
0
0
5
4
3
1
0
3
0
3
3
0
5
0
0
0
1
3
2
3
3
3
5
3
0
3
0
5
5
5
0
4
0
2
0
0
0
0
0
4
4
1
5
0
0
3
2
0
0
0
5
2
0
3
4
3
0
2
4
4
0
3
0
0
5
4
1
0
1
3
3
1
3
4
0
3
3
1
2
0
1
1
5
3
5
4
2
5
3
4
3
0
1
0
4
2
4
2
0
0
3
0
0
0
1
0
0
3
0
2
3
0
0
3
1
0
0
3
0
0
3
3
2
0
0
0
0
3
1
2
0
1
5
1
1
5
0
3
1
0
2
0
3
0
0
0
2
0
1
2
2
0
1
1
3
3
5
4
0
0
0
0
2
5
3
4
5
1
4
0
2
0
0
3
0
3
1
0
0
2
4
1
1
4
2
5
0
4
3
4
3
1
0
2
3
0
0
2
0
0
0
5
0
3
0
1
0
0
2
0
0
0
3
5
4
0
2
3
1
0
0
5
0
2
5
0
0
0
0
4
4
4
2
0
0
3
2
5
4
0
0
0
3
0
3
0
2
3
0
5
1
0
5
0
0
1
0
4
0
0
3
1
0
2
2
3
2
5
1
2
1
0
0
0
0
0
4
1
5
0
0
0
4
4
0
0
0
1
4
0
0
3
0
5
2
4
4
3
4
4
2
2
0
4
2
3
1
3
0
0
3
0
1
1
1
4
2
5
1
5
0
4
0
3
0
0
3
0
5
3
5
0
0
3
5
0
2
2
3
5
3
0
4
0
1
5
0
4
3
0
0
3
4
1
2
2
3
0
4
0
5
5
1
0
5
4
1
5
0
4
4
1
5
0
2
1
0
2
3
1
0
0
2
1
5
5
0
2
2
0
5
3
2
0
0
0
3
3
0
4
3
0
0
0
5
5
2
2
4
0
0
0
0
3
1
5
4
2
4
4
3
0
0
0
0
2
4
4
3
3
1
5
0
5
0
1
3
0
1
1
0
2
0
1
2
0
0
0
0
3
1
0
4
0
2
0
3
2
2
3
1
5
1
0
2
3
0
5
0
0
3
4
0
4
0
4
5
0
3
0
4
1
0
4
0
2
5
1
2
0
0
4
3
0
3
0
3
4
0
2
3
1
2
1
4
1
0
0
3
2
5
4
4
3
4
0
0
3
5
0
5
3
1
4
2
0
0
0
1
0
0
3
0
0
1
1
0
0
1
0
0
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0
0
4
5
5
3
5
2
0
3
4
4
1
0
0
3
0
4
4
3
3
4
4
0
1
0
3
5
0
0
4
3
1
2
3
3
2
3
3
0
2
0
0
4
3
3
5
5
0
5
0
2
5
0
0
2
0
0
3
5
0
0
0
5
0
0
4
4
0
0
2
1
1
5
4
1
0
3
5
1
0
3
0
5
0
3
5
2
4
0
0
1
0
5
0
5
2
2
2
0
3
3
5
0
5
0
5
4
1
0
3
4
4
1
0
0
0
2
0
0
3
0
3
3
1
0
0
Answer 4
8%
3
0
5
0
0
2
4
0
1
0
4
4
0
3
0
0
2
3
0
3
4
0
0
4
4
2
4
3
4
0
0
1
3
4
4
5
0
0
2
5
3
0
5
3
2
4
4
5
5
0
0
0
2
5
1
4
2
3
3
3
4
4
0
5
2
0
5
2
0
3
0
0
4
0
2
2
0
3
3
3
3
0
4
3
3
5
0
5
3
2
1
0
4
0
4
0
4
0
3
3
0
1
0
4
4
0
3
3
4
0
5
5
5
5
0
1
0
0
1
3
3
5
2
0
5
1
1
0
3
4
4
1
2
1
4
3
0
4
4
0
2
5
2
0
4
1
0
3
0
0
0
3
5
4
0
4
2
0
0
0
1
0
3
2
0
4
3
5
1
0
4
1
5
0
5
5
4
4
0
3
5
3
0
5
1
2
2
0
3
2
2
2
2
4
0
4
5
5
2
4
2
0
0
4
5
0
5
3
2
0
5
0
1
4
4
5
0
0
0
0
0
0
0
0
1
5
5
0
4
1
3
5
3
5
0
2
4
1
0
5
5
3
5
0
4
3
0
5
0
0
1
0
3
3
4
0
0
4
4
2
3
0
0
0
0
0
5
2
0
1
2
4
2
2
5
2
2
1
0
2
0
4
2
4
1
1
0
4
5
0
0
3
5
0
0
3
4
3
4
4
1
5
0
1
0
1
5
0
4
5
3
5
0
1
3
5
0
5
1
2
0
3
0
1
0
3
1
4
5
4
3
5
0
1
2
4
5
3
0
3
5
3
4
2
3
3
5
5
0
4
3
0
4
3
3
3
4
3
3
2
1
2
3
5
4
2
1
2
3
4
3
2
0
0
5
3
5
0
3
5
5
0
2
2
2
5
0
1
4
3
0
1
3
0
0
2
3
3
2
1
0
4
0
4
1
5
1
0
4
1
1
2
2
0
0
0
2
3
3
3
2
0
2
0
0
3
5
5
2
5
2
5
1
1
4
4
5
5
4
5
0
1
3
2
0
5
0
3
1
4
4
1
0
0
5
0
2
5
0
4
0
0
2
0
3
0
4
5
3
3
0
1
1
2
4
0
3
1
0
0
4
2
0
2
0
0
0
3
0
5
4
5
0
3
4
0
4
3
0
3
5
0
4
4
0
0
3
0
4
4
3
1
0
3
3
1
0
2
3
5
0
4
5
5
5
4
2
3
2
0
4
0
3
0
4
0
4
3
4
5
3
3
5
4
0
3
5
1
3
0
0
0
0
5
5
1
2
5
4
5
3
0
3
1
0
3
0
0
4
0
5
4
0
2
1
0
5
4
5
5
0
0
2
0
3
0
4
4
4
0
0
3
0
4
2
5
0
5
4
0
4
1
3
4
0
0
4
5
0
5
1
3
5
5
0
2
0
0
5
3
0
3
5
3
1
1
2
3
3
2
4
0
1
2
2
0
1
3
0
0
4
0
2
1
3
5
0
4
1
0
1
1
0
0
4
0
3
2
4
1
0
4
0
4
0
3
3
0
5
3
3
0
2
5
3
4
0
5
0
3
1
2
4
2
0
3
3
2
0
4
4
4
4
2
4
2
0
0
0
1
2
2
3
1
3
1
0
2
3
0
0
0
5
3
0
0
5
4
3
3
1
5
5
1
4
3
1
3
4
3
0
0
4
4
3
0
5
4
5
0
5
0
5
0
0
5
2
4
5
4
3
2
3
1
5
5
0
4
3
0
4
4
3
2
0
0
2
4
5
0
0
4
2
1
2
5
0
0
5
3
0
4
0
2
3
1
3
3
0
3
5
0
0
5
3
0
0
1
1
1
3
0
3
2
5
5
3
3
0
0
0
0
1
5
4
3
0
5
0
4
0
2
2
3
3
5
2
1
3
4
5
3
5
0
3
2
5
0
2
2
3
5
3
2
3
5
1
0
1
1
5
4
4
5
5
2
5
0
3
0
5
0
0
3
3
5
5
0
0
3
4
0
1
4
3
4
0
3
3
0
0
3
0
5
0
3
0
0
2
5
1
1
0
3
2
4
0
5
5
1
1
5
5
1
3
0
3
0
4
5
2
3
3
4
4
1
0
3
3
1
5
3
0
0
0
5
3
0
2
1
0
4
5
1
5
0
3
4
0
0
5
0
0
5
0
0
3
0
5
0
3
5
2
4
2
2
4
1
0
5
0
5
2
1
0
5
4
3
0
1
2
3
2
3
0
4
0
4
3
0
3
4
4
4
0
0
1
1
2
2
2
2
4
5
5
5
5
2
3
0
0
1
4
0
5
5
0
5
4
3
3
3
2
0
5
5
1
5
2
0
3
0
3
3
1
0
0
0
0
1
0
5
0
5
5
0
0
1
3
0
3
0
1
0
0
3
1
0
1
5
3
1
0
4
5
0
2
4
5
0
3
3
2
0
5
3
0
0
3
0
2
2
0
0
3
4
5
4
3
2
0
0
4
0
5
2
5
5
5
0
4
3
0
4
2
2
3
5
0
4
0
2
4
0
1
2
2
5
2
3
0
1
5
3
2
4
4
1
5
1
3
1
5
3
1
3
4
5
2
0
0
3
0
3
1
0
3
3
5
5
5
3
4
3
0
2
0
5
3
5
0
3
2
3
3
0
4
2
3
5
0
0
0
0
0
3
1
4
0
0
4
0
0
0
4
2
3
4
1
2
4
5
0
2
5
1
2
3
2
5
4
3
3
4
5
5
5
2
3
4
0
3
3
3
1
3
0
0
5
0
1
0
3
5
5
1
5
0
0
5
3
4
4
0
4
5
1
5
2
2
2
0
2
2
0
3
3
5
3
1
4
5
4
2
4
3
5
5
0
2
3
1
1
3
2
2
2
4
3
3
5
2
3
0
2
4
3
1
5
2
0
4
5
0
1
3
4
5
4
0
5
3
2
0
3
2
5
3
0
0
0
5
0
3
0
1
2
5
3
5
1
2
4
1
5
3
3
4
5
2
1
4
2
0
0
3
3
0
0
2
5
2
4
3
5
1
3
0
4
1
0
0
4
4
5
2
0
0
0
3
5
5
3
5
0
0
3
5
0
3
3
0
3
1
2
0
1
4
5
5
5
3
4
0
2
2
0
2
4
0
2
2
1
5
3
5
5
2
4
0
1
4
0
4
0
3
2
1
2
0
2
0
5
2
3
0
0
0
5
1
2
5
0
5
2
4
4
2
3
0
3
0
3
5
0
4
2
5
0
3
2
1
0
4
2
4
3
5
3
5
2
0
2
2
3
1
4
1
5
0
4
4
0
0
0
0
0
3
0
2
4
3
2
4
4
5
5
1
4
3
2
5
1
3
0
0
3
3
2
3
4
1
3
0
0
1
5
0
5
0
0
5
4
4
5
4
2
0
5
3
1
5
0
3
2
2
1
0
0
3
5
3
5
4
4
3
0
4
1
1
4
4
3
0
0
1
0
3
3
0
5
3
0
4
3
2
3
3
2
2
4
3
2
5
3
2
4
0
0
4
0
5
3
3
2
5
3
5
2
3
4
3
2
1
5
0
5
2
0
0
0
3
2
0
3
5
0
3
3
1
3
0
5
0
5
0
3
4
4
2
3
2
5
3
1
5
3
2
0
0
2
0
2
4
2
4
5
5
5
2
3
5
4
1
1
1
2
0
3
3
3
0
3
4
3
2
3
0
2
2
4
0
4
3
0
3
5
4
0
3
0
0
3
4
5
0
3
1
0
3
4
0
0
0
1
2
0
3
3
3
3
3
1
1
5
5
5
5
3
1
3
0
0
1
0
0
1
3
2
0
3
0
5
2
5
1
3
4
1
3
0
4
0
2
0
4
5
5
4
0
4
0
3
1
2
1
3
0
1
2
2
5
5
3
0
4
2
5
2
0
5
3
0
5
5
3
0
3
1
1
3
0
3
4
5
3
4
0
0
4
4
3
0
0
4
4
5
3
3
3
4
5
5
5
4
0
3
0
2
1
2
0
4
0
4
0
0
0
3
3
4
2
4
0
2
3
3
1
5
0
5
3
2
2
4
3
5
4
5
5
3
1
2
2
4
4
2
3
2
5
5
3
0
5
2
4
5
5
4
4
4
4
0
2
0
0
3
1
2
4
3
0
4
1
0
2
3
3
0
4
1
3
0
3
3
0
1
0
3
0
0
1
0
3
3
2
0
0
0
3
4
4
4
4
5
0
0
4
4
3
1
4
1
4
0
2
2
0
4
4
0
1
3
3
3
0
1
3
2
3
4
5
0
1
1
4
0
2
3
3
4
4
0
0
5
0
2
1
5
5
3
5
0
0
5
3
0
0
4
2
0
5
2
0
5
0
5
5
5
3
0
1
1
4
3
0
5
3
0
1
0
1
4
0
0
0
0
4
5
3
3
2
5
3
4
0
3
0
1
5
2
2
3
3
3
4
0
0
1
4
0
0
2
4
4
0
0
3
4
3
5
4
3
3
4
5
4
5
1
4
0
2
5
3
3
3
2
0
0
0
3
0
3
4
0
5
0
2
0
0
4
5
0
4
0
5
2
1
0
0
5
2
4
0
4
0
0
4
2
4
3
3
2
0
0
0
3
3
3
0
2
1
2
0
3
4
0
2
2
0
0
0
5
0
0
3
1
2
2
2
5
1
2
5
3
4
5
2
5
2
3
1
1
0
0
2
2
5
4
4
3
4
1
3
2
4
0
4
5
1
3
4
5
0
5
3
4
0
2
0
5
4
0
1
4
0
5
3
3
3
5
0
0
2
0
1
2
4
0
3
0
0
0
4
4
2
0
3
3
3
3
3
0
5
0
1
5
3
4
3
4
5
0
3
4
3
0
0
0
3
4
2
0
0
0
5
0
5
1
0
3
0
3
5
0
0
1
1
4
4
1
5
3
5
0
0
3
1
0
1
2
1
0
5
0
5
5
0
2
1
1
3
1
3
2
0
4
3
0
2
2
4
2
3
2
0
5
0
1
5
1
0
0
0
4
3
4
1
0
3
3
3
2
3
2
0
0
1
0
0
0
5
2
2
3
4
2
4
0
1
3
4
3
4
2
3
0
2
2
5
3
4
3
3
0
4
0
5
2
0
3
0
2
0
0
2
1
3
4
3
2
2
0
0
1
0
4
0
1
3
2
3
4
5
4
3
3
3
2
5
4
4
0
5
0
3
1
3
4
3
4
0
4
5
2
3
5
0
5
3
0
5
2
5
2
0
3
0
5
3
0
3
2
3
0
5
4
4
4
3
0
2
0
0
2
4
1
0
3
3
1
0
0
0
4
0
0
0
2
1
0
3
4
3
3
3
4
3
3
4
3
0
3
0
1
5
3
1
4
0
3
5
0
5
5
2
1
2
5
2
0
0
4
0
3
5
5
0
1
3
1
5
4
0
1
1
0
4
0
5
0
3
4
3
0
3
4
3
0
0
3
1
0
0
2
5
4
1
0
4
3
0
4
4
5
2
3
5
4
1
5
0
0
3
5
5
4
1
0
3
3
0
0
4
1
1
4
1
4
4
4
3
0
0
3
3
0
2
5
5
5
0
4
0
4
5
0
5
0
0
3
5
1
5
5
4
2
0
3
2
0
2
3
5
0
1
0
3
3
0
4
3
2
3
0
3
4
0
0
3
5
3
0
0
1
0
5
2
4
1
4
0
5
3
4
0
0
2
1
3
0
3
0
3
4
5
3
5
2
5
4
5
0
0
5
5
0
4
4
1
5
0
3
0
2
2
4
0
3
4
4
0
2
5
5
0
3
3
2
1
2
1
2
3
0
5
0
5
0
0
2
3
0
0
0
0
3
5
1
0
3
2
5
4
5
5
0
0
3
2
0
0
2
0
0
0
0
3
5
5
5
1
3
1
1
4
5
0
0
5
5
0
3
2
3
0
3
0
4
4
0
0
0
0
3
0
2
3
2
1
0
3
3
4
4
3
5
5
0
0
4
4
2
0
3
0
4
1
4
2
4
3
4
5
3
0
5
2
2
1
4
3
4
2
2
3
1
3
4
2
5
3
2
1
5
2
0
0
0
2
2
1
0
3
5
0
4
0
3
5
3
4
3
5
3
4
3
3
4
5
0
4
5
2
5
0
1
0
2
2
1
0
5
0
4
3
2
3
0
1
3
4
0
0
1
2
4
0
3
4
3
1
4
5
0
3
4
5
2
0
2
0
2
0
0
3
5
0
1
4
3
2
3
1
0
1
4
4
3
1
2
1
2
0
0
0
0
2
1
0
5
5
5
5
2
3
0
4
1
0
0
0
5
5
0
5
5
0
0
1
0
2
1
0
4
2
0
4
4
3
5
0
5
0
0
4
0
4
5
3
2
5
3
3
4
5
4
5
4
3
0
1
0
0
3
5
1
2
0
2
0
3
0
5
2
4
1
4
1
0
4
2
4
4
3
3
2
3
0
0
0
2
2
2
5
2
5
5
2
3
3
3
0
3
3
2
4
0
0
0
0
5
0
4
0
1
2
4
5
5
0
0
0
2
4
1
0
2
0
0
1
0
0
3
2
5
0
3
2
5
3
3
2
5
0
5
4
0
5
0
5
4
3
0
4
2
1
5
0
3
0
3
0
0
0
1
3
5
3
5
5
0
3
0
2
0
2
4
0
4
4
4
4
5
2
1
2
4
0
0
2
4
2
0
2
0
5
0
1
0
4
0
2
3
0
3
5
1
1
3
0
0
5
5
3
4
3
0
5
4
5
5
5
0
3
4
3
0
4
3
3
1
4
1
4
3
2
5
5
0
4
1
0
5
0
2
5
0
3
3
2
3
0
4
4
1
1
1
1
0
3
5
2
0
3
5
4
0
0
0
3
1
5
4
3
5
3
4
0
5
0
5
2
4
5
0
0
3
0
0
0
3
0
1
5
2
4
5
0
0
4
3
3
1
3
1
1
2
1
0
4
0
2
3
2
3
5
4
0
2
5
0
0
0
4
0
3
4
0
0
4
0
5
4
0
4
2
1
4
3
5
4
1
5
5
3
3
1
3
2
0
5
0
5
5
5
3
0
0
3
5
3
1
2
4
3
5
4
3
2
0
5
4
5
5
3
1
2
4
3
4
5
0
1
0
0
2
1
0
3
4
5
5
4
2
3
3
4
5
4
3
0
2
3
4
0
5
0
0
1
5
0
0
3
2
5
3
2
4
3
3
0
5
0
0
1
1
5
5
4
0
4
3
5
2
0
3
0
1
0
4
3
0
3
5
2
5
4
0
0
5
2
4
5
5
3
0
4
5
5
3
4
5
0
5
0
1
2
3
2
0
4
2
1
1
3
2
4
0
3
4
0
5
0
0
1
0
0
1
3
4
5
1
5
3
4
5
0
2
0
5
0
3
3
0
5
2
3
3
2
5
0
0
5
4
0
2
5
4
0
3
3
0
4
3
0
5
0
3
3
0
3
3
3
1
4
0
3
5
1
3
2
0
3
3
2
0
0
1
3
0
2
1
5
0
0
4
4
2
0
4
4
0
3
4
1
2
4
0
0
4
2
2
2
0
2
1
1
0
3
1
3
0
3
0
5
0
3
5
4
5
5
3
5
5
5
3
5
5
0
3
2
0
2
3
3
2
1
0
0
1
1
5
0
0
3
3
3
0
4
5
4
4
0
1
1
0
5
0
4
4
4
4
0
0
2
5
0
4
3
5
3
0
1
5
3
3
3
5
0
2
4
2
0
2
0
0
2
3
0
5
1
3
1
0
0
1
0
3
3
3
2
4
0
2
0
2
5
0
3
3
4
5
0
4
3
0
0
0
3
3
3
3
3
2
3
1
3
4
5
2
5
4
0
3
2
4
5
4
4
4
2
3
0
4
3
1
0
1
5
2
4
5
2
2
0
5
3
0
0
5
1
3
0
1
0
2
3
4
0
5
4
2
5
0
4
1
2
2
4
2
3
0
2
5
3
0
4
5
4
3
2
2
0
0
0
0
4
3
5
5
4
2
2
0
4
0
4
1
4
4
0
0
3
0
0
0
0
1
2
0
1
0
5
0
4
3
3
0
5
1
0
5
4
2
5
4
3
2
5
0
5
5
5
0
0
4
5
1
1
3
2
4
5
3
0
0
4
0
0
0
3
4
4
5
1
4
3
0
0
2
0
0
4
5
3
2
5
5
0
2
0
0
5
1
3
5
0
0
0
1
0
1
3
1
0
5
5
5
2
4
3
0
0
4
0
2
0
5
4
3
4
0
0
4
3
2
2
2
1
2
3
4
0
3
5
3
1
3
3
2
3
1
0
0
2
3
5
0
4
1
2
2
0
0
5
5
3
0
4
2
2
4
1
1
0
0
5
2
4
0
0
2
3
3
0
4
5
0
4
0
5
0
5
0
5
3
0
3
3
0
3
4
0
5
4
2
4
0
1
2
1
0
0
2
4
3
5
3
0
0
4
0
0
4
0
3
3
0
0
0
4
5
3
3
3
0
3
0
3
3
5
2
2
2
5
2
5
5
0
3
3
4
3
5
0
2
0
2
3
2
5
4
5
3
2
5
5
0
0
0
0
0
5
5
4
5
3
4
4
5
4
4
3
4
2
5
5
2
4
0
2
2
2
4
1
2
3
2
2
0
1
5
3
4
0
0
0
3
0
2
4
4
0
3
0
0
0
5
3
3
4
0
1
5
0
5
2
4
5
0
1
0
5
5
0
5
4
4
5
1
3
4
4
4
0
2
1
1
5
1
5
2
5
2
2
2
1
1
5
4
3
0
4
0
5
3
4
4
0
0
2
5
3
1
5
1
0
0
4
5
0
5
4
0
5
2
4
1
1
4
5
0
0
3
3
1
3
0
0
0
4
0
1
4
4
0
0
3
5
0
0
1
4
5
0
4
2
0
0
1
0
0
0
2
0
3
2
5
5
5
0
5
4
1
4
3
0
5
5
3
4
0
Answer 5
8%
0
0
5
0
0
0
4
0
1
3
5
0
0
1
5
0
5
2
0
5
2
3
0
3
2
3
3
5
1
0
0
1
4
0
4
5
0
0
2
5
4
2
5
3
4
2
0
4
2
0
5
1
4
3
2
3
5
2
2
2
5
3
0
3
2
0
5
0
0
3
0
0
1
0
5
2
1
0
1
1
2
0
3
0
3
3
0
5
5
1
1
5
2
4
4
0
4
0
1
2
0
0
0
4
4
0
3
3
2
5
5
4
5
2
3
2
5
5
0
2
3
5
0
0
0
1
4
3
2
5
5
3
1
0
5
0
3
3
3
2
4
5
1
0
0
3
0
0
0
4
0
1
2
2
0
0
1
0
4
5
0
5
4
1
0
4
4
0
3
3
5
3
0
3
4
5
3
4
0
3
5
3
0
5
0
3
2
5
3
2
2
4
0
3
3
3
5
3
4
3
1
0
0
5
3
2
0
2
3
0
5
0
1
2
2
3
0
2
4
2
0
0
0
0
1
4
3
2
2
3
4
0
5
3
0
3
2
4
1
1
3
2
5
5
3
3
5
5
3
0
3
1
2
3
3
0
2
3
0
3
5
0
0
0
0
0
5
4
5
0
4
5
2
1
1
0
1
0
0
4
5
2
4
3
2
0
5
4
5
0
0
3
5
3
0
3
3
2
3
0
4
5
2
5
0
2
0
0
3
5
0
3
0
1
5
2
0
1
4
0
3
1
0
1
4
2
0
5
5
4
3
1
5
5
2
4
0
1
1
4
4
1
0
4
1
2
4
1
0
4
2
0
3
3
1
4
2
3
3
5
1
2
5
5
2
1
4
0
0
5
3
0
5
4
5
0
5
0
2
5
5
0
1
0
3
4
3
5
1
2
1
2
3
0
0
0
1
5
3
2
5
4
0
3
0
0
2
0
4
4
2
3
4
0
0
0
3
0
0
4
3
0
4
0
0
0
0
4
3
5
0
5
1
1
3
5
4
0
2
0
2
1
5
2
5
4
5
5
3
3
0
1
3
0
1
0
0
4
0
5
5
4
4
0
2
0
1
3
1
3
0
1
4
1
4
1
0
1
0
0
2
5
3
2
5
0
0
3
0
4
0
4
0
5
0
0
2
4
4
2
4
5
4
2
3
0
4
2
2
4
0
2
0
5
5
0
0
5
2
2
4
3
4
3
3
2
2
3
1
0
5
0
0
0
0
0
2
0
3
3
3
4
4
4
0
4
5
0
0
0
3
5
0
3
5
0
0
2
2
2
2
2
4
0
1
3
0
0
2
1
5
3
0
0
5
3
5
4
3
5
3
2
0
3
0
1
0
4
2
0
0
2
0
1
3
4
5
3
3
5
0
3
5
2
0
2
5
5
0
5
0
3
5
4
0
3
0
4
2
5
5
5
5
4
4
3
0
3
0
4
0
1
4
3
2
5
0
5
2
0
4
1
2
0
2
3
0
5
2
0
4
0
0
2
2
0
4
3
5
3
0
4
3
4
0
1
4
3
1
3
0
0
1
5
0
1
0
4
0
1
4
1
3
1
1
4
2
5
3
3
2
5
4
5
0
1
5
0
0
1
4
3
4
3
2
3
0
4
0
5
0
0
3
1
3
0
0
3
5
1
3
5
5
1
2
1
1
3
5
0
0
0
4
1
3
0
4
3
1
4
5
0
2
1
0
5
5
0
5
2
5
3
0
2
5
5
5
0
2
0
5
3
2
0
4
0
3
3
5
2
1
1
2
1
2
3
0
0
3
2
0
1
0
2
3
2
1
4
5
4
0
1
2
4
5
0
5
1
1
1
3
1
4
1
5
1
4
1
0
3
0
0
0
3
2
2
5
5
0
3
2
0
1
1
2
5
0
0
3
5
5
4
3
2
5
3
0
2
2
1
5
2
2
4
3
2
0
5
0
1
4
3
4
2
5
4
4
0
2
0
5
0
5
4
5
5
5
0
4
5
5
0
0
3
4
3
4
2
0
3
4
4
0
5
0
5
0
0
2
4
1
1
4
5
4
3
1
4
5
0
0
5
3
3
3
4
0
2
2
4
0
3
3
0
2
0
5
0
0
0
3
3
5
3
0
5
5
1
3
0
0
4
2
2
2
2
0
2
3
0
5
3
3
5
0
3
2
0
5
3
0
4
2
3
3
5
5
3
0
5
5
5
3
4
0
4
4
1
3
1
2
5
3
2
5
2
0
4
0
5
5
5
0
5
0
0
1
5
4
1
0
1
0
5
0
3
5
4
3
0
0
1
3
5
4
4
0
3
2
3
2
1
2
0
4
3
0
4
5
0
2
5
3
5
2
4
3
2
0
1
0
5
0
3
4
5
0
5
2
0
5
5
2
0
0
4
0
0
5
0
1
1
0
3
5
0
2
5
4
0
5
2
0
4
0
0
5
0
5
0
3
3
0
1
0
2
0
1
3
1
4
5
0
0
0
1
3
5
0
0
1
0
0
3
1
2
3
3
0
4
0
4
4
2
0
4
2
4
1
0
0
2
2
1
2
0
0
3
3
0
0
0
4
1
1
3
4
5
2
4
1
4
0
3
2
5
4
4
3
4
0
5
1
1
0
2
0
5
4
0
3
4
1
0
5
0
5
1
5
2
0
1
4
0
0
4
1
1
2
0
3
0
0
3
0
5
4
3
4
2
3
5
2
4
5
2
0
3
1
0
4
2
0
5
2
4
5
2
1
3
4
0
5
2
1
2
4
0
3
4
4
4
0
4
5
1
1
3
3
5
0
4
4
2
2
1
1
0
1
4
1
0
5
0
5
3
0
2
3
2
3
5
4
3
2
5
5
0
0
3
2
5
1
2
1
3
2
0
3
1
5
1
0
0
3
2
5
2
3
0
0
3
4
0
4
2
1
0
5
4
3
2
3
0
2
5
2
3
3
0
2
5
0
2
0
3
2
0
3
3
0
2
4
1
4
5
4
5
3
5
3
3
4
0
0
3
4
0
5
3
0
1
5
3
5
1
1
0
0
3
0
0
0
2
3
3
0
0
0
2
4
5
2
5
0
0
1
2
3
5
4
0
3
1
0
0
1
5
0
0
5
1
5
4
3
3
4
0
3
2
4
0
5
4
3
5
5
5
3
0
3
0
4
5
0
2
2
0
3
2
0
0
0
2
2
0
5
4
5
3
3
5
0
1
5
2
3
0
0
0
0
0
3
1
0
4
5
2
5
2
2
1
5
5
0
2
2
5
3
5
4
3
0
4
4
1
4
0
5
0
5
5
0
0
0
0
2
3
5
5
3
1
1
5
5
5
5
2
4
0
1
5
1
0
0
0
0
5
1
5
4
2
5
0
0
2
5
0
5
0
3
0
2
2
5
4
2
4
5
0
1
3
0
3
5
3
2
4
0
2
5
1
5
1
4
4
0
0
1
1
3
1
3
1
0
4
1
1
3
0
5
5
0
5
1
4
4
3
2
5
2
1
3
5
4
4
0
0
0
4
0
4
3
4
1
2
3
2
3
4
3
5
1
2
4
2
4
0
5
5
2
0
4
4
0
1
2
4
3
3
4
0
5
0
5
3
0
5
5
5
3
3
5
1
4
4
4
0
3
0
4
0
2
5
3
3
5
4
4
2
4
2
4
4
2
4
5
0
0
0
1
0
4
3
3
0
1
0
1
3
5
0
5
1
0
4
4
2
0
2
0
0
1
4
3
1
5
4
4
1
4
0
0
0
0
1
0
1
0
0
2
5
2
2
4
5
3
5
4
1
3
0
0
0
0
0
0
4
1
0
2
5
0
3
5
0
1
3
3
3
0
3
3
4
0
2
0
3
4
3
2
0
2
1
0
4
0
0
2
2
1
4
0
4
0
3
5
5
5
0
3
3
5
0
4
2
4
5
4
4
2
0
0
5
5
0
4
0
5
0
2
3
1
2
3
5
3
4
2
5
0
5
2
2
2
0
5
5
5
2
0
0
5
0
2
0
2
2
4
0
3
2
2
1
4
4
3
0
5
0
0
0
5
5
4
5
2
5
2
5
3
0
2
2
5
3
4
1
4
2
4
4
4
5
3
1
0
0
0
2
4
0
2
3
4
4
3
1
0
0
2
4
0
2
0
1
3
1
0
2
2
4
2
3
1
2
1
0
4
0
1
0
0
3
1
2
2
4
0
2
0
4
5
5
4
0
0
5
5
0
2
3
0
5
0
1
3
0
2
3
0
2
2
1
5
0
2
2
3
2
0
3
0
2
1
1
5
1
4
4
5
1
0
5
2
0
1
1
5
1
0
5
5
4
4
3
5
3
4
1
5
5
4
0
5
0
4
0
5
2
0
4
1
5
3
4
5
5
0
3
0
1
4
0
0
0
5
2
0
0
0
2
5
3
4
4
2
0
0
5
4
4
0
4
3
1
1
0
4
3
0
0
0
5
2
0
0
5
4
5
0
0
5
3
4
1
4
3
0
4
0
3
0
0
2
5
4
0
0
5
1
0
3
2
0
0
3
3
4
0
3
2
0
2
0
5
2
0
3
3
5
4
3
2
3
0
0
3
1
3
3
1
1
5
1
0
3
3
1
0
3
2
0
1
2
4
5
4
5
0
4
0
0
5
0
0
4
1
1
1
5
3
1
5
1
2
0
1
5
3
5
3
0
0
0
3
1
4
0
3
4
5
0
3
2
3
4
0
2
0
1
0
2
2
0
4
2
0
0
5
3
5
5
1
1
0
5
5
5
3
2
0
0
3
0
2
2
4
4
1
0
0
0
0
4
4
0
2
3
3
5
0
0
5
5
3
0
0
4
3
4
0
0
5
2
5
0
3
0
3
2
0
4
0
0
4
2
3
0
0
3
0
5
5
0
0
3
3
4
0
0
3
3
5
0
0
5
3
0
1
1
0
4
5
0
5
0
2
0
4
1
3
5
3
2
0
5
5
0
1
5
5
3
4
5
0
2
0
5
4
1
0
1
2
0
0
5
1
5
3
5
0
0
4
5
5
0
5
0
0
5
4
2
3
4
0
1
5
3
2
4
4
4
3
4
3
0
5
5
5
4
3
5
5
0
1
0
5
1
1
3
4
4
0
0
4
4
5
5
3
0
5
0
0
2
4
2
3
3
2
2
4
5
5
3
3
3
4
0
4
5
5
3
4
5
5
1
5
4
5
1
5
5
5
1
3
2
0
5
1
2
3
2
5
0
0
5
3
3
3
0
3
0
3
0
4
2
4
4
5
0
5
0
0
0
5
0
0
3
5
1
1
4
2
5
5
3
0
2
0
3
4
0
4
4
1
5
3
4
5
0
0
5
0
0
3
2
2
4
0
5
3
0
3
0
1
4
4
4
3
0
3
4
0
3
5
5
0
1
4
2
4
5
0
2
1
1
5
0
4
5
2
5
2
0
0
5
5
4
3
4
5
4
5
4
4
3
0
5
3
2
4
5
5
3
0
0
5
0
1
5
0
4
0
0
4
4
3
0
3
5
5
5
4
3
0
5
5
3
4
3
1
2
5
5
3
5
2
5
4
5
0
2
5
5
5
0
5
0
0
4
2
2
4
3
3
2
5
0
1
1
4
5
3
4
3
3
5
0
0
2
5
0
4
3
4
4
3
0
4
1
3
0
4
3
0
3
0
5
1
4
0
5
1
3
0
0
5
0
3
0
4
0
4
2
4
4
0
5
3
4
3
3
0
5
3
0
5
5
3
3
0
4
4
3
0
3
4
0
5
4
0
4
3
0
5
1
0
2
3
0
1
2
1
0
0
4
5
0
0
2
3
0
0
0
5
1
0
1
0
3
1
5
4
0
4
0
0
2
1
0
0
5
5
0
4
5
3
2
5
5
4
2
5
3
4
5
4
3
5
3
5
4
3
4
3
2
4
0
0
5
3
0
3
5
2
4
2
3
0
0
2
0
0
4
3
5
0
0
4
0
4
1
0
4
5
5
5
3
3
5
5
2
5
0
3
5
0
2
2
1
1
0
5
1
4
1
5
0
3
5
3
1
2
5
2
1
0
1
0
4
1
0
0
5
0
3
4
3
3
3
3
3
5
3
4
5
4
1
5
0
0
5
5
5
5
1
0
0
4
2
0
4
0
5
2
1
4
0
5
1
3
0
0
4
5
3
0
0
3
2
0
0
4
0
0
4
5
2
0
2
0
2
0
0
5
5
0
4
5
1
3
4
3
0
1
5
3
4
5
0
0
1
0
0
1
0
3
2
0
3
5
0
0
2
2
4
0
0
3
0
2
3
5
0
4
5
0
0
0
5
1
1
1
5
0
0
0
5
4
5
0
5
1
0
3
5
3
4
3
3
3
5
5
2
4
4
5
3
4
0
3
5
2
4
5
3
5
0
4
0
5
2
0
3
4
3
5
0
4
5
0
3
5
4
4
5
2
2
0
0
5
4
4
4
1
0
5
1
4
4
3
2
4
4
2
5
0
0
1
0
3
0
4
0
0
0
3
5
5
0
0
5
1
3
2
5
0
0
0
4
0
0
3
1
5
2
5
1
4
4
3
0
3
4
5
4
5
5
3
5
1
4
3
3
0
3
1
0
1
0
5
0
2
0
3
0
5
2
0
1
0
1
3
0
0
0
5
0
5
3
5
0
4
4
2
5
3
0
5
0
2
3
0
0
3
5
0
0
0
0
0
0
2
0
4
5
2
4
0
0
3
2
0
1
1
3
0
0
2
3
3
3
0
3
3
4
0
5
4
3
1
5
2
3
4
1
5
5
0
5
0
0
0
1
1
5
0
1
5
5
5
5
4
5
0
0
1
2
3
0
5
2
1
2
2
4
5
4
4
3
2
5
2
4
5
4
4
0
4
5
5
2
5
0
3
3
2
0
5
0
4
0
2
4
3
1
2
0
0
3
1
3
3
4
3
1
1
0
0
0
5
0
3
3
0
5
0
0
5
5
3
0
0
3
4
1
2
0
4
3
0
4
2
4
5
5
4
1
2
0
5
3
3
4
4
0
4
3
3
0
2
0
0
4
5
3
0
0
3
5
3
1
1
3
4
2
3
3
1
0
3
3
3
2
1
1
5
2
0
5
5
0
3
0
0
5
0
0
3
1
3
5
4
3
4
3
5
5
3
3
2
2
4
2
5
0
5
0
1
0
4
2
2
3
2
5
2
3
3
3
0
5
3
0
0
3
4
5
4
1
0
3
4
4
0
2
0
2
0
5
5
0
5
3
5
5
0
0
4
5
5
1
2
2
0
0
3
5
4
1
5
4
0
5
0
3
1
4
3
0
4
4
3
5
3
0
4
0
2
3
0
0
5
0
1
0
0
1
3
2
1
4
0
4
4
5
0
0
0
2
5
0
4
2
3
1
4
3
5
3
0
0
4
3
1
1
5
4
4
4
5
0
4
2
0
5
0
4
5
0
1
4
5
1
2
0
3
5
1
4
5
4
4
3
0
0
0
2
4
0
2
2
3
0
5
5
0
1
0
4
0
5
2
4
5
4
5
5
0
4
0
3
2
0
2
1
0
5
3
5
3
0
3
0
4
5
4
5
0
4
4
5
5
5
3
3
0
2
3
2
4
0
5
5
4
4
1
0
4
2
0
3
5
0
0
3
3
4
5
3
5
3
0
4
1
4
5
0
5
4
4
0
3
5
2
5
2
4
5
1
4
0
3
3
4
4
4
3
1
0
3
4
0
4
4
1
5
5
3
5
0
3
1
5
0
0
0
3
3
3
2
5
0
0
0
4
5
0
5
1
4
4
4
3
2
0
5
5
1
2
0
3
3
1
3
1
3
0
4
2
5
4
0
3
1
2
4
0
3
0
2
0
0
2
2
1
0
3
0
1
3
5
3
4
4
3
5
2
0
5
1
5
0
1
1
4
4
3
0
5
2
3
3
2
2
1
4
4
0
1
4
0
2
0
5
0
5
0
3
4
1
0
0
5
4
5
5
1
3
5
0
0
0
0
0
5
5
2
0
4
5
2
3
0
1
0
5
0
2
1
1
5
4
4
4
4
5
3
5
0
1
0
5
4
2
4
0
3
0
4
5
4
2
2
5
1
1
4
5
4
2
5
3
4
0
4
3
0
0
0
2
3
3
5
0
5
4
5
0
0
2
5
3
4
2
0
5
5
0
1
5
5
5
2
0
5
0
0
3
1
0
1
1
2
5
4
5
5
1
0
2
3
0
5
3
3
0
1
1
3
0
5
3
3
5
5
2
0
2
1
3
5
0
4
2
2
1
5
4
3
4
4
0
0
5
4
5
3
5
2
1
1
0
0
4
4
2
5
3
0
2
1
2
5
4
0
3
4
4
2
0
0
2
1
0
0
5
0
5
0
0
3
5
0
4
5
5
0
3
5
0
2
3
0
3
3
4
0
1
0
3
0
0
1
1
5
5
5
0
3
1
3
3
3
3
0
2
3
3
0
3
4
2
5
3
0
3
4
0
2
5
1
5
5
0
4
3
4
0
1
4
5
5
3
0
2
0
3
5
3
5
5
5
0
4
0
0
0
0
4
0
0
0
0
2
1
4
3
5
5
0
0
3
3
5
4
4
4
1
5
0
1
1
0
0
1
4
3
5
5
2
5
3
5
0
0
5
4
4
1
1
4
4
2
0
0
2
4
5
5
5
0
1
0
5
5
2
1
5
0
1
0
5
3
3
5
2
4
0
3
1
3
3
5
3
3
2
4
1
3
3
3
3
2
0
3
0
2
5
4
2
1
5
5
0
0
4
0
0
3
0
1
2
1
5
2
0
5
3
4
3
5
4
0
5
4
3
3
2
1
5
3
4
0
1
4
3
3
0
3
0
3
4
3
0
0
2
2
4
0
5
2
3
0
0
3
1
2
0
1
4
0
4
2
4
3
0
3
4
0
1
5
3
0
0
4
4
4
3
1
0
1
Answer 6
6%
4
0
0
0
0
0
5
4
1
0
2
0
5
5
3
0
1
2
0
2
2
5
0
0
0
4
4
0
0
0
0
0
0
3
5
3
0
0
2
0
5
0
3
3
3
0
0
5
0
0
0
0
2
2
4
5
3
5
5
5
0
4
0
1
3
0
5
0
3
0
0
3
2
0
0
3
1
2
2
2
2
0
4
0
1
2
0
4
5
1
1
3
5
0
0
0
5
0
1
3
3
1
0
0
0
0
5
3
2
0
0
1
5
1
0
1
5
0
4
5
3
1
0
2
1
3
4
2
3
5
0
0
5
1
0
0
0
0
3
0
2
5
5
0
0
3
0
0
3
0
0
3
3
4
0
2
5
3
0
5
4
0
0
3
3
2
0
0
2
0
4
5
0
0
5
0
2
2
0
1
5
1
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4
0
4
0
0
0
1
3
0
0
0
3
0
0
4
1
3
4
0
0
0
3
5
0
2
0
3
0
0
0
0
0
0
1
0
5
2
2
2
0
4
0
5
0
0
2
4
0
0
2
0
0
3
0
4
3
4
0
4
5
4
1
5
1
2
2
4
4
4
4
3
0
4
3
0
0
0
0
1
3
2
5
0
3
1
0
0
0
2
0
2
5
0
3
3
5
3
3
0
0
5
3
5
2
1
5
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
4
3
0
1
3
5
0
2
4
1
3
5
0
1
0
0
5
0
0
0
4
0
5
0
0
0
5
1
0
5
4
0
1
0
0
0
4
1
2
4
3
4
3
1
4
2
0
0
4
5
2
3
0
1
4
0
0
0
3
0
3
0
1
0
0
1
3
3
1
2
2
0
2
3
3
2
0
3
5
1
0
1
3
2
3
1
5
5
0
0
0
0
0
2
0
2
5
3
0
3
0
4
3
5
4
2
2
0
2
2
2
3
4
0
0
5
0
0
3
0
4
3
4
1
1
2
2
0
1
1
4
0
3
0
5
4
0
4
2
3
4
5
2
4
3
0
5
2
0
4
3
5
5
0
0
4
5
0
1
1
1
5
0
4
5
3
0
5
0
4
2
0
2
3
3
5
0
5
0
1
1
2
0
3
0
0
4
0
4
0
0
0
0
0
4
5
4
1
0
0
4
2
3
0
0
4
5
0
0
4
4
4
0
1
4
5
0
0
0
3
5
2
1
0
5
0
5
0
0
0
4
5
0
4
1
3
0
0
2
4
2
2
0
3
5
1
5
3
0
2
2
0
0
0
0
4
2
0
3
0
0
5
5
5
0
4
5
0
0
2
1
0
4
1
5
0
2
0
2
5
0
2
1
3
0
4
2
0
0
5
0
4
0
5
5
0
3
5
1
0
1
0
5
5
2
0
2
0
0
0
5
3
5
0
0
0
3
0
0
5
0
0
1
5
0
2
0
5
5
0
0
1
0
5
0
4
0
0
0
0
0
2
0
0
0
2
5
4
4
4
2
5
5
5
5
0
0
3
0
0
4
0
0
5
5
0
0
0
0
2
0
5
0
3
0
5
4
0
1
0
0
4
2
0
0
5
4
2
0
0
0
4
0
0
0
2
0
0
3
4
2
1
2
5
0
1
5
5
2
0
0
0
4
1
0
2
0
4
0
0
1
0
1
3
0
0
2
2
2
4
3
0
0
1
4
0
3
3
0
0
1
0
2
5
5
0
2
2
4
4
0
3
3
5
1
5
2
4
0
3
3
4
0
4
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
3
0
0
0
0
0
1
1
0
4
0
0
2
0
2
0
2
2
0
4
2
2
0
0
0
0
5
3
5
3
0
5
0
5
5
5
2
4
0
0
0
4
5
2
0
5
4
5
0
3
1
0
0
1
0
0
0
0
0
5
5
2
0
0
0
0
1
3
0
0
3
3
0
0
0
0
0
4
0
4
0
0
4
2
0
0
0
0
3
5
3
1
0
0
2
2
0
0
0
4
0
5
4
5
0
0
3
1
5
5
0
2
0
0
2
4
5
0
5
3
0
1
2
3
1
1
0
0
1
0
5
0
3
5
1
1
0
2
3
0
2
0
0
3
2
4
2
0
0
0
0
5
5
0
3
3
5
0
0
0
4
0
3
0
0
0
3
0
3
3
0
0
1
0
5
0
0
2
4
2
3
0
2
0
3
0
0
5
3
4
4
3
0
0
3
0
0
3
0
0
2
0
0
0
4
4
2
2
5
0
3
0
0
4
4
4
3
2
0
0
5
2
0
0
1
4
0
5
0
3
0
2
2
2
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
5
1
3
0
0
0
3
0
4
5
4
2
0
0
0
1
0
0
1
3
4
5
5
2
3
3
4
0
0
0
4
0
1
0
4
0
0
0
0
0
0
5
5
4
4
2
3
1
5
5
2
0
0
0
0
2
3
2
3
2
5
0
1
0
3
3
0
5
4
1
1
1
1
4
4
1
2
0
2
0
0
5
3
2
2
5
0
0
0
0
0
0
0
0
1
0
1
5
5
0
4
3
0
0
3
5
0
2
2
2
3
5
3
1
2
2
0
1
3
0
0
5
0
1
0
5
4
0
0
2
2
5
0
5
2
4
4
0
5
0
4
0
1
0
0
5
1
4
5
0
3
1
0
4
5
4
0
0
4
3
5
3
2
0
0
Answer 7
6%
0
0
0
0
0
0
5
3
1
0
2
0
4
5
4
0
0
0
0
2
2
5
0
0
0
4
2
0
3
0
0
0
0
3
5
4
0
4
2
0
5
4
2
4
1
0
2
5
5
0
0
0
4
2
3
5
5
3
5
5
0
5
0
4
3
0
5
0
3
0
0
0
2
0
1
4
4
1
3
3
3
0
3
0
2
2
0
4
5
1
0
3
4
0
0
0
5
0
3
4
3
1
0
0
4
0
5
3
3
0
0
2
4
1
0
3
5
0
4
5
4
2
0
0
2
1
4
0
2
5
0
0
3
0
0
0
0
0
3
0
2
5
0
0
0
1
1
1
3
0
0
2
2
5
0
2
1
0
0
0
0
0
2
1
3
2
5
0
3
0
4
4
0
0
5
0
2
2
0
2
5
2
4
5
0
1
1
0
0
1
1
3
0
2
0
2
3
2
5
5
1
0
0
4
5
0
0
0
1
0
2
0
3
2
4
4
0
0
0
0
0
0
0
0
2
2
2
0
1
0
5
2
2
1
0
0
1
1
0
1
1
5
3
0
2
5
0
5
2
0
0
0
0
2
0
0
5
5
3
0
0
2
0
0
0
0
3
1
0
2
1
4
4
0
4
4
3
0
0
0
5
4
3
3
0
0
0
0
2
0
0
3
0
5
0
2
2
0
3
0
1
4
4
1
0
1
0
0
4
3
0
4
0
0
5
0
2
0
3
0
0
1
3
0
4
5
0
5
0
0
5
4
0
5
1
3
0
4
2
4
0
0
1
5
2
2
3
2
0
2
0
0
1
3
5
0
1
5
1
3
1
2
4
5
0
4
1
0
2
4
2
0
0
0
5
0
3
0
1
5
1
3
0
0
0
3
0
0
5
0
0
1
2
0
4
1
0
2
5
1
2
5
0
2
0
0
1
3
3
4
3
2
4
0
0
0
3
0
0
1
3
0
5
0
1
0
0
0
1
5
0
3
1
1
3
0
0
0
0
0
3
0
2
1
3
4
0
0
0
0
0
5
4
0
5
0
0
4
1
2
5
0
5
4
0
1
0
5
2
5
0
3
3
0
0
4
0
2
2
0
0
4
0
4
1
0
0
0
0
0
0
1
0
1
0
0
0
3
0
2
4
5
5
4
5
0
3
0
4
4
4
1
0
4
1
0
2
3
2
3
2
0
4
4
0
2
5
5
0
0
4
0
0
0
0
0
3
0
0
5
3
3
3
0
0
0
5
0
0
3
0
0
0
2
3
1
3
3
0
4
0
0
4
0
4
4
0
0
2
0
2
0
1
0
0
0
3
3
0
3
0
0
1
5
0
0
0
5
3
0
0
3
3
0
3
3
4
2
3
0
0
4
3
2
0
0
4
4
0
5
3
0
2
4
0
4
0
4
2
5
1
5
1
1
5
4
3
4
0
0
0
0
1
4
2
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
3
2
0
0
1
3
0
5
2
2
0
0
0
0
0
1
3
0
5
5
1
0
4
0
0
2
0
1
0
2
0
1
0
1
0
2
2
0
3
1
1
4
2
5
4
0
0
0
0
1
0
3
4
5
1
3
0
4
0
0
0
0
4
2
3
0
0
4
1
0
4
3
0
1
4
4
3
3
1
1
0
0
0
1
3
0
0
0
1
3
3
0
0
3
0
4
4
0
0
0
5
5
0
0
4
5
0
0
2
0
3
5
0
0
0
0
3
2
4
4
4
0
4
2
3
4
0
0
0
4
5
1
0
2
4
0
5
1
0
2
0
0
4
0
5
0
0
3
1
2
1
3
3
3
3
0
2
0
4
0
0
0
0
3
1
4
0
0
0
2
2
0
0
1
4
0
0
0
3
0
4
4
3
4
0
3
0
3
1
0
4
1
4
5
3
1
0
0
0
1
2
2
4
2
5
1
2
0
4
0
3
0
0
2
3
5
3
5
1
3
3
0
0
3
1
5
3
2
0
0
0
1
5
0
0
3
0
0
2
3
1
3
2
5
4
4
0
5
5
3
0
5
4
1
3
0
0
3
0
5
3
0
1
0
4
0
1
0
0
0
2
4
0
0
0
2
0
5
5
0
0
0
3
3
4
0
4
1
4
0
0
2
3
1
0
0
0
0
0
0
0
3
5
3
3
1
2
5
0
0
0
5
2
1
4
0
3
1
5
2
5
0
1
3
0
4
0
0
1
3
0
4
0
0
0
0
4
2
3
1
3
3
0
5
0
3
3
1
5
3
0
2
1
0
4
4
0
1
4
4
4
2
5
0
0
3
0
5
0
0
3
0
2
4
1
0
0
0
5
4
0
0
0
3
4
0
5
4
4
0
2
0
4
0
0
3
2
4
4
0
2
3
0
0
1
0
0
3
3
0
5
2
0
0
0
1
0
0
3
0
0
3
0
2
0
3
0
0
0
0
2
3
0
0
0
0
2
4
0
3
3
0
0
5
1
0
1
0
0
3
0
5
2
0
0
0
0
3
1
0
0
1
5
1
3
0
0
0
0
0
0
0
3
3
0
0
0
1
4
0
0
5
0
4
5
0
1
3
4
5
0
5
1
3
4
3
5
0
1
0
1
0
2
0
5
0
2
1
4
4
3
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
3
2
4
4
1
4
0
0
2
3
0
0
2
0
3
3
3
2
3
5
5
0
5
0
0
0
1
4
2
4
2
0
5
0
1
0
3
0
3
0
0
0
5
0
0
4
0
0
3
0
3
0
3
2
0
0
5
0
4
1
3
5
4
0
3
5
4
5
1
0
4
0
0
2
2
1
0
4
3
0
0
0
3
1
1
0
0
0
0
5
5
2
0
0
0
3
4
0
4
0
4
2
3
0
5
1
0
0
3
4
3
1
0
0
0
4
3
1
0
1
4
0
0
5
1
3
2
1
2
5
3
1
5
4
1
3
4
0
0
3
1
0
0
0
0
0
5
4
5
2
3
0
0
0
0
0
0
2
1
2
0
0
5
4
3
5
3
2
0
0
3
2
5
5
4
0
5
0
0
0
0
0
0
0
2
1
2
3
2
2
5
2
5
0
4
0
1
0
4
4
3
0
5
0
5
0
1
0
0
0
3
2
0
2
4
0
0
3
2
0
4
0
5
4
1
3
0
0
5
3
1
1
0
0
0
0
5
1
0
0
4
2
0
0
1
2
0
0
5
4
2
4
1
5
3
0
0
5
4
0
5
3
4
0
3
0
0
0
0
0
0
1
0
5
3
0
0
3
0
2
4
2
5
0
4
3
1
0
0
0
0
3
1
5
1
0
0
0
0
4
3
0
2
0
0
0
2
1
0
5
2
0
3
0
1
4
4
1
5
5
2
3
0
3
3
4
0
1
4
3
0
5
1
4
4
3
5
0
0
0
0
1
0
0
4
4
1
0
0
0
2
2
2
1
2
1
0
4
2
3
0
0
0
4
0
0
4
3
1
1
0
4
1
3
4
0
1
5
3
0
3
4
0
2
0
0
4
0
0
1
3
4
4
1
3
0
3
0
2
0
0
4
2
1
1
5
5
3
4
0
2
0
0
0
3
0
3
2
0
2
3
5
5
1
0
0
3
2
3
0
0
0
5
0
1
0
5
0
4
1
5
0
1
4
0
0
3
2
0
5
0
1
0
1
0
0
1
0
5
0
0
2
0
1
4
0
0
0
0
1
0
0
3
0
3
2
0
2
5
3
3
0
0
0
2
0
0
1
3
3
2
3
2
0
1
0
3
4
2
0
5
1
0
2
0
5
1
2
5
5
4
1
3
0
4
0
0
2
0
5
0
0
3
1
0
2
0
3
0
0
3
1
1
0
5
5
0
0
0
3
1
3
2
5
5
0
0
3
0
0
0
0
0
0
1
0
0
4
0
5
0
3
0
1
0
3
3
1
3
1
5
1
3
0
0
2
0
2
1
0
0
0
5
0
1
4
3
0
4
3
3
4
4
5
0
0
5
3
4
1
2
4
3
1
0
5
2
3
0
2
1
1
5
4
0
3
0
3
4
0
0
0
0
0
3
0
3
4
0
0
2
0
0
0
1
0
0
0
5
2
3
3
0
4
1
0
0
3
0
5
0
0
4
0
0
0
0
3
0
4
0
0
0
0
0
3
2
0
0
0
0
4
4
0
4
3
1
1
0
2
0
0
0
2
1
0
4
3
0
0
3
2
2
0
0
4
0
3
3
2
0
1
0
1
4
3
0
0
2
3
3
1
0
5
4
5
0
2
5
0
0
5
3
0
0
3
3
0
4
0
0
0
3
3
0
3
5
0
0
5
5
5
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
3
0
4
0
5
3
1
4
5
0
1
0
0
5
5
0
0
3
3
0
0
0
2
3
0
0
2
2
1
0
5
0
0
0
0
3
0
0
0
3
4
0
0
0
0
0
3
1
0
0
3
1
0
1
0
4
0
5
0
4
3
0
0
4
0
1
3
4
4
0
4
4
4
3
3
0
2
0
0
0
2
4
1
0
5
2
2
0
1
4
0
4
5
0
2
0
0
0
0
0
1
0
0
1
3
1
0
0
0
0
0
3
2
3
4
0
0
0
1
4
5
1
0
0
0
4
0
4
4
3
0
0
2
0
1
0
0
0
0
2
0
0
0
0
4
5
0
1
0
0
0
2
4
1
2
0
0
1
0
5
4
5
3
2
0
0
5
0
2
0
0
4
3
5
1
5
0
5
0
5
0
0
4
4
2
0
2
4
2
5
0
4
0
4
3
0
0
0
0
0
0
5
0
0
0
0
4
0
0
0
2
1
5
3
2
0
2
1
0
0
5
1
5
1
3
4
5
3
0
3
4
3
0
5
2
4
4
0
2
0
3
3
4
0
1
1
0
0
5
0
3
0
5
0
4
0
0
0
0
1
1
4
0
0
4
0
2
2
1
0
0
4
4
5
0
0
0
3
4
0
1
2
0
1
0
1
2
2
0
3
0
5
5
4
3
2
4
0
0
0
0
0
3
1
4
0
0
0
0
0
3
5
0
0
0
5
0
0
3
0
3
0
0
1
3
4
5
0
0
3
1
0
3
0
0
3
4
4
3
0
2
5
5
3
2
0
0
2
2
4
1
0
5
0
0
0
4
3
0
3
5
0
3
3
0
3
0
5
0
3
0
3
4
1
0
1
0
0
0
3
0
0
3
0
0
2
0
0
3
3
3
0
1
0
0
4
0
3
5
3
4
0
5
0
2
5
0
5
4
3
4
4
3
0
5
3
0
3
0
0
3
5
5
0
0
2
1
0
3
5
4
0
3
4
3
1
1
0
4
4
0
4
0
1
3
5
2
0
0
0
0
0
0
0
4
0
0
0
5
5
4
0
3
2
4
0
0
4
5
5
0
4
2
0
0
3
1
0
0
0
3
0
1
2
5
0
1
3
2
0
5
2
0
1
0
4
1
0
0
2
0
4
3
3
3
3
3
0
3
4
0
2
0
5
3
0
1
3
2
3
3
0
4
2
0
5
3
3
0
1
3
0
0
0
1
4
3
0
3
3
5
0
0
0
1
0
0
0
2
0
3
0
3
1
2
0
2
1
4
0
0
5
4
5
0
2
4
5
1
0
4
4
4
5
1
0
3
0
5
0
2
2
0
4
0
3
5
0
1
0
5
2
0
2
5
0
1
3
0
1
3
4
5
1
0
1
1
0
2
0
0
0
0
0
1
4
4
0
0
0
1
0
2
2
1
1
4
2
3
3
0
0
5
0
5
0
0
0
5
0
3
2
0
0
3
2
2
3
1
0
1
1
0
4
4
0
5
0
1
0
4
0
0
0
0
4
0
0
1
0
0
3
2
0
0
0
0
0
0
3
0
0
0
0
0
2
4
5
1
3
0
4
0
3
4
0
3
3
0
0
5
0
3
3
4
0
0
0
3
3
5
3
2
0
1
5
1
0
0
3
3
1
0
0
4
0
0
0
1
0
2
0
5
2
3
1
0
0
5
5
5
3
2
5
0
0
4
4
5
0
4
0
4
4
3
1
5
0
2
4
0
3
0
0
0
3
0
1
0
4
4
5
0
1
0
5
2
2
0
0
2
5
4
0
2
2
4
0
0
5
0
2
5
5
2
4
3
5
2
0
0
4
5
0
0
2
4
0
3
0
4
4
0
0
0
4
0
0
5
1
1
3
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
4
5
3
5
2
1
0
0
1
0
3
3
0
3
3
5
5
2
4
2
4
1
5
0
5
5
0
0
5
1
2
0
5
0
4
0
0
4
2
4
3
0
0
4
0
2
4
3
0
3
4
2
0
0
4
4
2
4
2
0
4
3
0
4
3
0
0
0
3
3
0
0
1
0
1
0
3
0
5
2
3
3
3
0
0
0
0
0
3
0
2
0
4
4
0
0
2
3
3
4
5
0
0
4
2
0
4
0
3
0
0
3
0
5
0
4
4
0
1
1
2
5
3
0
3
0
0
0
5
0
0
0
0
3
0
1
0
1
0
0
3
5
0
0
5
0
0
3
1
4
4
0
0
0
2
5
0
2
0
3
0
0
0
0
0
0
2
0
5
2
2
3
0
1
0
3
0
0
1
5
0
0
2
0
4
3
0
5
2
4
0
4
5
4
1
4
1
1
1
4
4
4
4
4
0
5
3
0
0
0
0
3
2
2
4
0
3
1
0
0
0
1
0
0
5
0
3
3
5
4
4
4
0
5
3
5
1
2
5
1
0
0
0
0
0
2
0
0
3
4
0
2
0
0
2
0
0
4
4
0
0
0
0
0
2
4
4
3
2
0
0
0
0
0
5
0
3
3
0
0
0
0
0
4
0
0
0
2
0
1
3
0
1
3
0
2
3
2
3
4
0
5
2
0
0
4
4
3
4
5
1
2
1
0
0
0
0
3
5
1
0
0
2
2
3
1
1
5
2
2
2
2
2
0
3
4
3
0
0
5
4
3
2
5
5
0
2
0
4
0
1
5
2
2
3
0
2
0
3
3
5
4
1
0
0
3
2
5
4
0
0
0
2
0
0
0
0
5
3
4
1
1
2
3
0
4
0
0
0
2
0
3
4
2
0
3
3
2
0
3
0
0
0
5
2
0
5
3
5
5
0
2
5
5
0
2
2
1
4
0
4
1
3
0
3
4
5
1
0
1
1
3
5
0
4
0
3
4
2
0
3
0
0
4
0
3
0
0
0
0
0
4
4
4
2
2
0
4
3
3
0
0
4
5
0
0
4
0
3
0
1
4
4
3
5
0
2
5
2
3
0
1
0
0
5
0
0
4
0
0
0
2
2
0
0
1
4
1
2
0
3
5
0
4
2
0
3
2
1
3
0
2
2
2
5
5
0
0
0
5
0
0
0
4
0
0
2
1
0
4
1
0
4
1
0
3
5
0
2
1
0
0
2
3
1
0
5
0
3
0
5
4
1
3
4
2
0
1
3
5
5
2
0
0
4
0
0
5
2
3
0
5
2
3
0
0
5
0
0
1
5
0
1
4
5
4
0
1
1
0
5
0
4
0
0
0
0
0
1
0
0
0
2
0
3
0
1
1
5
4
4
5
0
0
0
0
0
3
0
0
4
2
0
0
0
0
3
0
5
0
3
0
5
4
0
3
0
0
0
2
0
0
4
1
0
0
0
0
4
0
0
0
2
0
1
2
4
1
3
4
5
0
1
2
5
3
0
0
5
0
3
0
2
0
4
0
0
1
0
1
0
0
0
2
2
3
4
4
0
4
2
1
0
2
2
0
0
1
0
2
4
5
0
3
5
4
3
0
0
3
3
3
0
0
1
1
3
0
5
0
5
3
0
1
0
0
0
1
2
0
2
3
0
4
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
4
0
3
2
1
2
0
5
1
0
4
3
0
0
0
4
0
5
2
3
3
0
5
0
5
4
4
4
0
0
2
1
4
5
1
4
3
4
5
0
0
1
0
1
1
1
0
0
0
0
5
5
0
0
3
0
5
1
2
0
0
3
5
0
0
0
0
0
0
0
4
0
0
5
2
0
4
0
0
4
3
3
2
0
0
2
2
0
0
0
4
0
5
0
4
0
0
3
1
1
4
0
5
1
0
3
4
4
4
5
2
0
1
4
3
2
1
0
0
1
0
5
0
4
5
1
1
0
2
3
0
3
0
0
3
2
4
0
0
0
0
0
5
2
0
3
0
5
0
0
4
3
0
2
3
4
0
5
1
3
4
0
0
3
0
0
0
0
0
5
3
4
0
3
3
1
0
0
5
1
3
4
3
0
0
4
0
0
3
0
0
2
0
0
0
4
0
0
2
5
0
3
0
0
3
4
4
0
2
0
0
5
4
0
0
3
4
0
4
0
4
4
2
1
3
5
1
0
0
3
0
0
0
0
0
0
0
0
0
3
0
4
3
2
3
0
0
3
2
0
4
5
2
1
0
1
0
1
5
0
1
4
4
5
0
1
3
3
3
0
0
0
3
0
1
0
3
0
0
0
0
0
0
5
5
5
4
0
0
0
4
4
1
0
0
4
0
2
3
0
3
0
5
0
1
0
2
5
0
0
2
3
1
1
2
3
4
1
2
0
1
0
0
5
3
1
0
5
0
0
0
0
0
0
0
0
0
0
1
4
3
0
0
3
0
0
3
4
0
1
3
2
1
5
3
2
2
3
0
1
3
2
0
4
2
2
0
4
4
0
0
1
1
5
0
5
2
5
3
0
5
0
4
0
1
0
0
5
0
0
5
0
3
1
0
0
0
1
1
0
4
0
5
3
4
0
0
Answer 8
6%
0
0
0
0
0
2
2
0
1
0
3
0
0
0
0
1
0
1
3
5
2
0
1
0
0
2
5
0
5
3
0
0
0
0
5
2
0
0
1
0
5
0
4
2
1
0
0
4
4
0
0
0
3
0
2
2
2
4
4
4
0
5
5
3
2
0
0
3
0
0
0
0
1
0
0
4
0
0
4
4
3
0
5
0
1
5
0
5
5
1
0
0
5
0
1
0
2
3
2
5
1
1
2
0
1
0
1
2
2
0
0
3
4
4
0
1
0
0
0
3
2
4
0
1
2
3
3
0
2
3
0
1
1
1
1
0
0
0
2
0
2
5
1
0
0
3
1
0
0
0
3
0
1
0
0
2
1
0
2
0
0
5
3
1
0
1
0
0
0
0
2
3
0
0
1
0
3
3
0
1
0
4
0
0
0
2
1
0
0
1
3
3
0
1
0
3
0
5
1
5
1
0
0
5
5
2
0
1
1
0
3
2
1
3
5
2
0
0
4
0
0
0
0
2
2
4
2
0
3
0
3
2
2
2
1
0
3
3
0
2
3
4
5
3
4
1
0
5
0
0
0
0
0
1
4
0
0
2
0
0
1
0
0
0
0
0
3
4
0
0
1
4
3
1
1
2
3
0
0
0
5
0
0
1
0
0
2
0
1
0
0
2
0
0
0
2
3
2
3
0
2
5
0
1
0
1
0
0
2
3
0
2
0
1
5
0
0
0
1
0
0
1
0
1
0
2
0
3
0
1
2
4
3
5
1
3
1
0
0
4
0
5
0
2
0
4
1
2
0
2
0
4
4
4
4
0
3
3
0
0
1
1
5
5
4
0
1
3
0
5
2
0
3
0
5
1
5
5
2
5
5
1
1
0
1
2
0
3
2
0
2
1
4
0
0
2
0
1
5
1
0
3
0
2
0
0
1
0
1
2
1
2
2
0
2
0
2
1
5
2
3
2
1
0
0
0
4
0
3
5
0
5
1
1
2
5
1
0
0
0
2
4
2
2
0
4
0
0
0
4
0
2
0
0
4
4
0
1
1
1
0
2
1
3
0
0
2
3
1
3
0
1
1
0
0
0
0
2
3
0
0
3
0
2
2
0
0
3
3
0
0
3
0
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3
0
0
4
0
2
0
0
2
1
1
2
0
0
4
4
4
2
0
3
4
0
0
4
1
5
1
5
2
5
1
0
0
1
5
0
1
0
3
0
0
0
0
0
2
0
3
3
1
1
0
0
2
2
0
1
0
4
3
1
1
2
0
3
3
0
0
0
2
3
0
0
3
0
0
3
2
0
0
0
5
0
0
1
3
0
5
2
0
0
1
2
4
1
0
2
1
3
0
2
0
1
0
5
0
2
0
4
0
0
4
5
2
0
2
0
4
3
2
0
4
0
0
0
4
4
3
0
0
3
4
1
0
4
0
0
3
5
0
3
5
3
3
0
4
1
0
5
0
3
3
4
0
0
0
0
0
1
3
4
0
5
4
1
2
5
3
3
0
0
1
4
2
0
3
0
3
1
1
0
0
0
0
1
0
0
2
0
2
5
2
0
4
0
0
4
2
0
1
3
1
3
0
0
0
0
0
0
0
3
0
0
1
2
0
2
5
3
0
1
2
5
1
0
1
3
3
2
0
1
3
4
0
0
1
0
1
0
5
0
1
3
4
3
4
4
2
2
0
0
3
1
0
0
1
0
3
3
1
4
3
2
2
5
2
3
0
1
1
0
2
2
0
3
1
0
0
3
0
0
1
2
1
0
0
2
0
2
0
0
1
0
1
0
0
2
0
3
0
2
1
0
0
0
1
2
0
0
0
2
1
0
0
2
1
0
2
1
0
0
0
0
0
5
4
0
2
1
0
0
0
4
5
2
0
0
3
3
1
1
0
1
0
3
3
0
0
1
0
0
0
1
2
2
0
1
4
5
0
0
0
0
0
0
0
0
0
3
5
0
0
0
0
0
0
0
5
5
0
5
1
0
1
2
0
3
4
5
2
1
0
1
3
0
3
0
4
0
4
0
3
1
0
3
2
2
4
0
1
3
3
4
4
0
0
3
1
2
2
5
1
2
1
0
0
2
0
1
0
2
5
3
3
0
0
2
0
4
0
1
4
1
2
0
0
0
2
3
0
2
0
0
0
4
3
0
3
2
0
1
2
0
4
2
2
2
4
0
0
1
2
0
0
2
0
2
5
3
0
2
1
2
0
4
0
1
4
0
3
0
0
3
0
2
3
0
0
3
0
0
0
5
3
1
3
3
0
1
0
1
3
5
3
1
4
0
2
5
4
0
0
3
5
0
5
0
3
0
1
1
3
5
2
0
0
2
0
0
0
0
0
0
0
0
0
4
0
4
5
3
3
0
0
3
4
0
4
4
1
3
0
0
0
1
0
0
1
3
5
5
0
1
3
4
5
2
0
0
2
3
1
0
1
0
0
0
3
0
2
5
5
5
0
1
0
0
5
4
3
2
0
1
0
5
4
4
1
0
4
0
0
0
3
2
0
0
0
3
1
1
1
4
4
3
3
0
2
1
0
3
5
2
0
4
0
0
0
0
0
0
0
2
0
0
1
5
3
0
0
3
3
0
5
3
0
2
2
3
1
3
3
1
3
2
0
1
3
2
0
0
4
1
0
5
3
2
1
1
0
3
0
5
2
2
3
0
4
0
5
0
3
0
0
0
4
0
3
0
3
1
0
0
0
3
0
3
2
0
4
2
4
0
0
Answer 9
5%
0
0
0
0
0
0
1
0
1
0
2
4
0
0
1
3
0
0
0
5
4
0
0
0
1
5
5
0
2
2
0
0
0
0
3
1
0
0
1
0
5
1
5
3
0
4
5
5
3
0
0
0
2
0
2
3
4
1
1
1
0
5
0
1
2
0
0
4
0
0
0
0
0
0
0
2
0
0
2
4
4
0
5
0
0
5
0
5
4
0
0
0
5
0
0
0
0
0
0
5
1
0
2
0
0
0
2
3
4
0
0
0
2
3
0
2
0
0
0
0
1
5
0
0
3
3
0
0
1
3
0
0
1
0
0
5
0
4
0
0
1
5
0
0
0
2
1
0
0
0
0
3
1
0
0
0
0
0
0
0
4
0
3
0
0
1
0
0
0
0
0
0
0
5
0
5
3
1
0
0
0
2
0
0
0
2
1
0
0
0
2
3
0
3
0
0
0
5
2
4
0
0
2
5
2
0
0
4
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
2
5
4
0
3
0
3
5
2
0
0
0
1
3
0
5
0
1
0
0
0
0
5
5
0
2
0
0
0
1
0
0
0
1
0
0
3
0
3
0
0
0
5
0
0
0
1
3
1
0
0
1
2
0
0
0
0
0
2
3
0
0
5
0
1
0
0
1
0
0
0
1
4
2
3
0
3
2
0
1
0
4
0
0
2
4
0
3
0
0
1
0
0
0
1
2
2
1
2
0
0
2
0
1
0
2
0
4
0
5
1
3
0
0
0
5
0
2
0
0
0
5
1
1
0
2
0
0
3
5
0
5
5
0
0
0
3
0
5
5
0
0
1
0
3
4
5
4
0
0
5
2
5
0
1
5
1
0
0
0
1
5
0
0
4
0
0
1
0
0
0
1
2
0
0
0
5
3
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
4
0
2
0
3
3
0
0
4
5
0
0
1
1
0
0
1
0
0
0
0
5
1
0
0
4
0
5
0
0
3
0
0
0
5
0
0
1
0
1
0
0
3
0
0
0
0
4
2
3
3
3
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
4
0
1
3
0
0
5
0
1
0
0
5
4
0
0
4
0
4
0
0
1
0
2
0
0
1
1
0
1
0
0
0
3
0
5
2
1
0
0
3
3
3
0
0
0
4
0
0
5
3
1
4
0
0
0
1
0
0
3
0
0
0
5
3
0
5
2
0
3
0
0
1
0
0
3
0
0
5
0
0
0
0
0
0
0
5
0
0
5
0
0
1
0
0
0
0
3
0
0
4
2
1
0
1
2
0
1
1
0
0
0
4
3
0
0
2
3
0
0
0
0
5
2
0
3
0
0
1
2
0
2
3
2
3
4
0
1
0
3
0
0
3
4
3
0
4
1
0
0
3
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
1
3
5
0
0
0
0
3
0
0
0
5
3
3
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
1
2
0
3
4
0
0
0
0
1
0
0
0
1
1
0
0
5
0
0
0
0
3
3
0
0
0
5
1
1
1
1
0
1
5
1
0
1
4
0
0
0
0
1
2
0
0
0
3
0
2
0
0
0
0
5
0
1
0
2
2
2
0
0
5
0
0
0
0
0
1
0
0
0
0
0
3
4
3
0
1
0
5
0
0
2
0
0
5
2
0
4
0
1
5
0
0
0
0
3
0
0
0
4
4
0
0
0
1
0
1
0
1
1
4
5
3
1
0
0
0
0
0
3
1
0
1
0
0
3
1
4
0
0
5
0
1
0
3
0
5
3
4
3
0
1
0
0
0
2
5
5
0
2
5
1
0
0
0
1
4
3
0
0
5
0
2
0
0
3
0
0
0
1
0
5
5
0
2
2
3
0
0
4
0
3
0
1
0
0
0
0
0
4
0
1
0
0
0
2
1
0
0
2
3
3
0
4
1
0
0
5
3
2
4
3
0
0
0
2
0
3
0
0
0
0
1
0
0
1
5
1
0
0
0
5
0
0
3
0
0
0
0
5
2
0
0
4
0
0
0
0
0
3
0
0
0
0
5
0
0
5
1
3
0
0
1
2
0
0
1
5
1
2
0
0
4
0
5
1
0
0
1
2
0
5
0
0
0
0
3
3
0
0
0
0
0
3
0
1
0
1
0
5
0
3
4
2
5
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
2
3
4
1
0
5
2
0
1
0
0
0
1
0
5
0
3
5
0
0
5
2
0
2
0
3
0
0
2
0
0
5
0
1
0
0
0
1
0
0
4
0
1
0
2
0
5
0
0
0
0
4
0
5
1
0
0
0
1
0
4
0
0
0
0
0
0
2
0
2
5
0
0
0
0
0
5
3
0
1
0
0
0
0
5
4
0
0
0
0
5
0
0
0
3
5
1
0
0
0
0
0
0
0
2
1
2
0
0
4
5
3
0
0
2
0
2
0
0
4
2
2
0
5
3
1
0
0
5
1
0
0
0
0
5
4
0
0
0
2
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
2
0
3
5
2
0
0
5
0
2
1
0
2
1
4
0
0
5
0
0
0
1
0
1
1
1
0
5
3
0
0
0
0
3
0
0
0
2
0
0
0
4
0
0
0
2
0
1
3
0
0
0
0
0
3
0
1
5
3
5
0
1
2
5
0
3
0
0
3
0
3
0
0
2
3
0
0
3
1
5
0
3
3
0
2
3
5
0
0
0
5
0
0
4
0
0
0
1
0
5
1
0
0
3
3
5
0
0
0
0
5
0
4
0
1
2
0
0
2
0
2
0
2
5
1
3
1
4
5
0
4
3
0
0
0
2
3
0
0
5
0
1
2
5
2
3
0
3
5
0
0
0
0
0
3
0
0
0
0
4
0
1
3
3
0
3
5
0
5
0
0
3
0
0
0
0
0
0
0
1
1
2
1
1
4
3
0
1
1
5
0
2
0
4
4
1
0
2
0
5
0
0
3
0
0
2
0
0
0
0
0
0
1
3
0
1
0
1
1
1
3
0
0
1
1
3
0
0
0
0
0
3
3
0
0
0
1
0
1
1
1
5
0
4
2
1
5
2
5
5
0
3
5
2
0
1
2
5
0
1
0
0
0
0
0
0
2
0
0
0
1
1
2
0
5
4
4
2
0
2
5
0
0
0
0
0
1
0
1
1
0
0
0
0
2
5
0
4
0
0
0
3
1
0
5
5
0
5
1
5
5
0
5
5
5
4
0
0
3
0
1
5
0
4
4
0
1
1
1
2
0
0
0
0
0
0
4
0
0
4
1
0
1
0
0
3
0
1
1
2
0
3
4
3
3
0
0
0
5
0
0
3
4
2
1
0
0
0
2
1
5
1
4
5
0
5
0
0
1
2
0
4
0
0
1
0
1
1
4
3
0
0
0
5
0
0
4
3
2
1
1
5
0
0
3
1
0
0
0
1
0
0
2
0
1
0
5
5
3
0
1
4
1
0
0
3
0
3
0
1
0
1
0
3
2
1
0
1
1
3
0
3
1
0
1
0
0
0
4
0
0
1
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
1
5
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
3
2
0
0
0
0
0
2
1
1
3
0
3
0
5
1
2
0
1
0
5
1
0
1
5
0
2
0
5
0
0
0
0
0
5
0
3
0
2
5
5
5
3
0
2
0
0
0
1
0
1
2
1
3
0
4
2
0
0
0
0
0
0
1
0
0
0
0
5
0
1
0
3
0
5
2
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
4
1
4
0
1
0
1
1
1
0
0
0
0
0
5
2
3
0
0
0
5
4
0
3
0
0
0
5
0
1
5
2
1
0
0
5
5
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
4
0
0
0
0
1
3
1
0
2
1
0
0
5
1
1
0
0
0
0
0
2
0
3
4
0
0
0
0
4
0
5
2
0
5
0
0
5
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
3
0
3
0
1
0
1
0
0
0
3
0
1
0
0
2
0
0
0
5
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
4
1
0
0
0
5
5
0
0
0
0
4
0
0
0
0
0
0
5
3
2
4
0
0
1
2
0
0
4
1
0
2
0
1
0
1
0
0
5
0
0
4
4
4
0
0
0
2
1
0
0
4
0
0
0
5
4
1
0
0
0
0
0
3
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
5
0
1
0
0
0
0
0
1
2
0
3
0
5
5
2
4
3
0
4
0
0
0
4
2
0
0
0
1
1
0
3
3
0
1
0
0
0
0
5
0
0
0
2
0
2
1
3
1
0
1
0
0
0
2
4
4
1
0
0
0
0
1
2
5
0
0
0
5
0
2
0
3
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
5
4
1
2
0
0
0
0
0
5
3
3
4
0
0
3
0
2
0
0
0
3
5
1
0
0
5
5
2
1
0
2
5
2
0
0
2
2
3
0
5
0
2
1
0
0
0
0
3
0
0
0
0
0
0
5
0
0
0
0
1
5
0
0
2
3
5
0
0
5
0
0
1
1
0
0
2
0
5
4
4
3
1
1
0
5
0
4
0
1
3
5
0
5
3
0
0
4
0
0
0
1
0
3
0
0
3
0
1
5
0
0
0
0
0
0
1
5
0
0
2
0
0
5
0
0
4
5
0
0
2
0
4
0
1
1
3
0
4
0
5
5
0
4
4
4
4
0
0
0
0
1
0
3
0
4
0
0
0
1
4
5
0
0
3
0
0
0
3
4
0
0
1
3
0
5
0
1
3
1
0
2
4
0
4
1
4
0
4
1
3
5
4
3
0
0
4
2
1
0
0
5
0
0
0
4
0
2
0
4
0
2
4
0
5
3
5
0
5
0
0
4
1
0
0
0
0
2
3
0
0
3
0
0
0
0
0
5
5
0
0
5
0
0
4
0
1
0
0
4
4
5
0
3
0
1
0
3
2
5
1
2
0
5
3
0
3
0
0
1
2
2
0
0
3
1
0
0
5
5
0
0
3
4
5
0
0
3
0
1
3
0
2
5
5
3
0
0
0
0
0
0
0
2
4
0
0
3
5
4
0
0
0
1
0
4
1
5
0
0
5
3
0
0
0
0
0
0
0
2
0
5
1
5
5
0
4
1
0
1
0
0
0
0
3
0
0
0
1
0
0
4
5
5
0
2
0
5
4
0
4
0
0
3
0
0
5
0
4
2
0
0
1
0
3
5
0
0
0
0
0
0
0
1
5
0
0
4
4
2
5
5
0
4
0
0
5
1
0
3
0
5
1
3
1
1
1
3
0
0
3
1
3
5
0
0
0
1
0
3
3
1
5
1
0
0
0
4
0
0
5
0
1
4
0
5
0
5
0
0
0
0
4
2
0
5
5
0
0
1
0
5
1
0
1
3
0
0
0
3
5
0
0
0
1
0
0
0
0
3
0
1
0
3
2
5
3
5
4
0
0
0
2
0
0
0
4
0
0
0
3
0
5
1
0
0
3
1
3
0
1
0
5
1
0
5
0
0
0
0
1
0
0
0
0
0
0
5
0
5
4
5
0
0
0
0
0
0
4
5
0
0
0
0
1
1
0
3
1
0
1
2
1
5
0
1
2
0
0
3
0
0
0
1
0
0
0
1
4
0
5
0
0
0
3
0
0
0
0
0
0
0
0
4
0
0
1
5
0
0
0
5
4
3
0
0
3
1
2
3
0
4
5
0
0
0
0
4
0
0
0
0
0
2
0
4
0
3
1
0
1
0
0
3
1
0
0
2
1
4
0
0
0
0
0
0
5
0
0
1
2
2
0
0
0
0
0
0
5
0
2
0
1
5
0
1
0
0
1
0
0
4
5
0
1
0
1
0
0
0
0
1
4
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
3
0
0
0
5
4
3
0
3
0
0
0
0
3
4
0
4
3
2
4
2
3
4
4
0
2
5
2
0
2
0
2
1
1
4
0
0
3
1
0
2
2
2
5
0
2
5
4
0
1
1
0
3
4
0
0
0
5
3
3
5
0
4
5
0
0
4
4
0
0
0
2
5
0
0
2
0
1
0
4
0
0
1
0
5
3
0
0
0
0
2
1
0
0
0
1
0
0
0
0
4
4
3
3
0
5
2
1
0
5
0
5
0
0
1
0
5
0
5
0
0
1
0
0
0
0
0
0
0
0
0
1
0
5
0
0
1
0
1
0
0
0
0
5
0
0
5
3
0
0
3
1
5
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
1
0
3
0
1
0
0
0
0
1
0
0
5
5
0
0
0
0
0
4
0
3
5
0
0
0
2
3
1
0
0
5
0
0
4
5
0
2
0
0
0
0
0
0
0
1
5
3
3
0
4
4
3
0
0
0
4
0
5
4
0
1
5
1
0
0
0
2
0
5
1
0
3
0
0
0
0
0
0
2
4
1
0
0
0
2
0
0
2
0
0
5
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
5
0
0
3
0
5
0
0
0
5
0
0
0
0
0
1
5
0
0
3
0
5
1
0
0
1
0
0
2
3
0
0
5
5
1
0
1
1
0
0
0
0
0
3
5
0
0
0
3
5
0
1
0
5
5
0
4
3
5
0
5
3
4
0
3
0
1
3
2
2
5
0
0
0
0
0
1
3
4
3
1
0
3
0
5
1
0
2
1
0
0
3
0
1
0
0
5
0
0
0
0
0
2
0
4
0
0
2
3
3
0
3
0
0
0
0
0
0
4
0
0
5
5
1
0
2
0
0
3
3
2
0
5
1
0
5
0
4
0
5
0
0
2
0
0
0
1
2
5
0
2
0
0
5
0
1
1
1
3
0
1
1
2
2
4
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
2
0
0
1
4
2
4
0
0
1
5
0
4
0
5
0
3
1
5
1
0
0
2
5
0
1
0
2
4
0
0
0
0
4
0
4
0
1
0
0
0
3
2
0
1
0
3
5
0
3
1
0
1
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
4
0
5
1
3
3
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
3
5
0
5
5
2
3
0
5
5
5
5
2
0
2
4
5
0
0
5
0
0
1
3
3
0
0
0
5
0
0
0
0
5
0
3
5
0
5
3
3
0
3
1
0
4
0
5
5
5
0
0
0
0
4
1
1
5
0
3
0
0
3
2
3
4
0
0
1
0
0
0
1
0
0
0
5
0
0
0
0
1
0
0
0
0
2
5
5
0
5
0
0
3
4
5
0
1
0
1
0
0
0
2
0
0
4
2
0
0
0
0
3
1
3
2
0
5
0
5
0
3
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
5
3
3
0
1
0
3
0
3
5
5
0
2
0
1
3
4
0
5
1
3
3
0
1
0
1
2
0
3
4
0
1
3
0
0
3
0
0
1
0
0
5
0
0
0
4
0
0
2
0
0
0
0
3
0
5
0
0
1
0
0
0
0
5
0
0
0
0
1
0
0
5
4
0
1
2
0
0
0
0
0
5
1
1
0
0
0
0
0
5
4
5
0
0
0
4
0
4
0
4
0
1
5
0
0
5
0
0
0
2
1
0
0
0
5
2
0
0
0
0
0
0
1
0
0
4
5
0
0
0
0
3
0
0
5
5
0
1
3
0
1
0
0
5
5
5
2
0
0
4
3
0
0
0
2
0
2
5
2
0
0
0
3
0
2
0
0
0
0
1
1
0
0
4
1
0
0
5
1
1
1
0
0
0
0
0
0
5
0
1
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
3
0
2
0
0
0
5
1
4
5
5
0
1
0
0
0
0
0
1
2
0
0
3
1
1
0
0
1
0
4
5
5
0
4
4
0
0
5
0
3
1
0
0
0
5
5
2
3
3
0
4
0
0
3
5
2
0
2
0
0
5
2
0
0
3
5
5
5
0
4
0
1
4
3
4
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
5
5
0
2
3
0
5
5
0
4
4
2
4
0
0
0
1
0
0
1
2
5
3
0
1
5
3
5
2
0
0
2
3
1
0
1
0
1
0
0
0
5
5
5
5
0
1
0
0
4
0
0
0
0
0
0
5
5
3
1
0
3
0
0
0
3
3
0
0
1
5
1
1
0
2
5
5
0
0
0
0
0
1
4
0
0
4
0
0
4
5
0
0
0
2
0
0
0
3
5
5
0
1
0
0
5
5
0
5
1
4
3
0
3
1
0
0
0
4
3
4
0
0
0
0
0
4
1
1
0
1
0
2
0
0
1
1
2
0
1
0
0
0
0
5
0
0
0
0
0
0
3
1
0
0
0
4
0
0
0
0
3
0
2
0
0
Answer 10
6%
0
0
0
5
5
0
5
0
2
0
4
2
0
2
2
3
0
2
5
5
3
0
0
4
3
2
3
4
4
0
1
4
0
3
3
1
0
0
0
5
5
0
5
2
1
2
0
0
0
0
4
0
3
0
0
1
0
2
3
1
0
4
5
2
1
0
0
5
0
4
0
0
5
0
0
1
0
0
3
4
4
0
5
0
3
5
0
5
4
1
0
0
5
0
3
0
5
0
0
5
0
0
5
5
1
0
0
4
3
0
0
0
5
5
0
2
0
0
1
3
2
5
0
1
5
1
3
0
3
0
1
0
5
0
2
1
0
4
0
4
3
3
1
0
3
4
0
0
0
0
0
1
5
0
0
0
0
0
0
3
0
1
1
1
5
5
0
0
0
0
5
2
0
0
5
0
4
2
0
4
5
2
1
5
0
2
1
5
3
2
5
3
0
3
0
2
0
5
1
5
2
0
0
3
5
0
3
0
0
0
3
0
1
4
5
1
0
3
0
0
0
0
0
0
3
1
4
0
2
0
5
1
3
5
0
1
1
1
0
3
0
2
3
5
0
2
3
5
0
5
4
0
0
2
4
0
0
2
1
3
0
0
0
0
0
0
0
3
0
0
2
3
1
0
1
4
1
0
0
0
0
2
3
5
5
0
0
0
2
0
5
1
0
4
0
2
4
1
3
0
4
5
0
4
0
1
2
2
2
4
5
3
0
0
3
1
0
0
0
1
0
3
2
0
0
1
0
2
0
2
0
5
0
1
1
2
2
0
0
5
0
5
3
1
1
5
5
3
0
2
5
0
1
4
2
0
5
3
0
4
0
1
2
5
3
0
1
2
3
5
4
0
4
5
5
0
3
0
4
3
3
0
0
0
2
5
5
0
5
2
1
1
0
0
0
0
3
1
0
0
0
4
0
2
1
0
3
0
0
4
4
0
1
0
0
0
2
0
4
3
4
0
0
0
0
0
5
0
5
5
3
4
0
1
2
5
5
0
0
0
0
5
4
4
0
5
0
3
2
5
0
0
0
0
1
0
0
4
0
1
0
3
2
2
3
0
3
4
0
1
0
1
0
0
3
0
0
1
3
0
0
5
0
0
5
0
5
0
2
0
1
2
0
4
0
5
0
5
5
2
4
0
5
4
0
0
4
0
1
0
0
1
0
2
0
0
3
3
1
0
0
0
0
5
0
4
5
0
0
0
3
0
0
0
5
0
4
2
0
5
3
2
3
2
0
2
1
0
3
5
0
0
0
5
5
0
1
5
3
3
1
0
4
0
0
0
0
5
5
0
0
2
0
5
0
5
4
4
0
3
0
0
1
0
3
0
0
4
5
0
0
4
0
0
1
5
0
2
1
0
0
1
3
0
3
0
5
5
0
5
0
0
1
3
0
4
2
0
2
2
1
1
4
3
1
2
1
3
0
3
0
0
2
4
3
0
3
5
0
0
4
5
0
0
4
3
0
3
0
0
3
5
0
0
1
0
0
3
0
3
0
0
0
0
0
1
0
0
5
3
0
0
0
3
0
1
0
5
0
2
3
1
1
3
0
1
3
0
0
4
0
1
2
4
5
5
0
0
0
0
0
0
2
1
1
2
0
3
1
3
0
0
5
5
1
1
0
5
1
2
2
0
5
1
3
5
0
1
1
0
2
1
0
5
3
0
0
5
2
0
3
0
5
0
0
5
0
2
5
5
1
2
4
0
3
0
4
0
1
0
3
2
1
3
0
0
1
4
4
3
0
3
3
1
0
2
0
0
1
0
0
3
0
1
4
5
0
1
0
1
0
0
1
1
1
2
0
0
1
0
1
0
1
1
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0
4
3
0
1
3
0
0
0
0
0
5
1
0
1
2
0
0
0
1
3
2
0
3
3
5
1
3
4
5
0
4
5
0
5
3
0
0
0
3
5
0
0
0
4
2
4
0
0
0
0
0
2
3
0
1
5
0
0
0
0
0
0
0
5
5
0
1
0
0
4
0
0
3
5
5
4
0
0
3
0
0
3
3
0
0
0
5
2
0
0
5
4
0
1
0
4
3
3
3
2
0
0
5
4
0
1
2
1
5
1
0
0
0
0
1
0
2
0
2
3
2
0
4
0
2
0
2
5
1
4
0
5
0
1
5
1
1
0
0
0
3
0
0
3
3
0
1
0
0
0
5
1
2
1
0
0
1
0
0
0
1
4
3
3
1
0
1
1
1
0
2
1
1
3
4
3
5
0
2
0
0
3
0
2
0
0
0
5
4
5
3
5
4
0
5
3
3
4
5
0
3
2
5
3
1
4
5
0
4
2
1
5
3
2
0
4
3
5
1
4
0
0
3
5
5
0
5
3
0
0
0
0
0
3
5
3
4
5
2
3
0
4
0
3
3
1
4
0
0
1
1
0
0
1
5
5
3
5
3
3
4
4
2
0
0
2
3
0
0
1
0
0
1
0
5
3
5
5
4
0
1
2
0
4
0
4
0
0
0
0
5
3
0
4
0
4
0
0
0
5
3
2
3
1
3
2
1
3
5
5
3
2
0
1
0
0
3
2
3
0
1
0
0
1
4
0
1
4
0
0
0
1
1
1
5
0
2
4
0
4
4
0
1
2
4
0
2
3
1
0
0
0
5
0
4
0
0
0
3
0
5
2
0
4
1
0
2
0
1
4
3
1
4
3
0
4
0
0
0
1
0
3
4
0
0
3
3
0
0
0
4
1
4
2
0
3
1
4
0
0
Answer 11
6%
0
0
0
0
0
1
4
0
1
0
2
0
0
0
0
0
0
2
0
5
3
3
0
0
2
1
4
4
2
1
0
0
1
0
4
0
0
3
1
0
4
0
3
4
3
0
0
2
3
0
0
0
3
3
2
1
2
4
3
3
0
5
0
4
1
0
0
0
0
0
3
0
2
0
0
1
1
0
3
2
2
0
4
0
3
5
0
5
3
2
3
0
0
0
1
0
2
0
0
4
0
2
0
0
2
0
0
4
4
0
0
0
4
4
0
2
0
0
1
1
3
5
5
0
1
3
1
0
2
2
0
0
5
0
3
0
0
0
1
0
3
5
1
0
0
3
0
0
0
0
4
0
0
0
0
0
2
0
0
0
1
3
1
1
0
1
0
0
2
0
3
2
0
0
5
0
3
3
0
0
5
1
0
0
0
3
1
0
0
0
5
4
1
2
3
2
0
3
2
2
1
0
0
5
5
4
0
0
2
0
2
0
1
3
2
1
0
0
0
0
0
4
0
0
1
2
3
0
3
0
5
3
3
1
4
1
3
2
1
2
2
3
3
0
4
0
0
1
0
1
0
0
0
3
5
0
0
4
0
0
0
0
0
0
0
0
4
4
0
0
1
3
2
0
1
4
2
0
0
0
1
2
4
2
0
0
1
0
5
0
0
3
0
0
0
2
4
0
3
0
2
5
4
1
0
2
0
1
3
5
0
1
0
0
1
0
2
0
1
2
0
3
0
0
0
4
0
5
0
0
1
4
0
2
2
2
0
0
1
3
0
2
1
0
0
4
3
2
0
4
0
0
1
4
4
2
4
3
3
0
0
1
2
5
0
0
1
0
3
4
2
2
0
0
4
0
4
0
4
4
3
0
2
0
1
4
0
4
5
0
0
1
3
0
4
0
4
1
3
2
0
4
0
3
0
0
3
0
2
3
3
0
2
0
0
2
1
0
3
1
4
0
5
0
0
0
0
0
3
5
0
3
1
4
1
0
3
0
0
3
0
3
0
2
0
5
0
1
0
0
0
1
0
0
5
0
0
3
0
2
0
1
1
0
0
1
3
4
5
2
0
2
2
0
0
0
0
2
2
0
0
5
3
1
4
0
0
0
0
0
5
2
0
1
0
0
0
5
3
2
2
3
4
3
2
0
4
0
1
0
0
2
0
4
0
0
2
3
5
1
0
0
0
3
0
3
3
2
0
0
4
0
4
3
1
0
3
0
0
5
4
1
2
0
3
2
2
0
0
0
0
0
5
4
4
0
3
0
3
5
1
0
4
0
0
2
0
0
3
0
0
0
0
1
1
0
4
4
0
4
0
0
1
4
0
0
0
4
4
0
0
3
3
1
1
5
0
2
3
0
0
4
3
1
2
3
5
2
0
5
2
4
1
3
2
2
0
0
2
4
2
5
5
1
2
4
1
1
0
0
0
0
4
3
2
0
1
5
0
0
0
0
0
0
1
0
0
3
0
0
2
3
0
0
3
0
0
4
1
1
0
0
0
0
0
0
5
0
1
4
1
0
2
3
0
2
0
2
5
3
0
1
0
2
0
0
3
3
0
4
3
3
3
2
3
0
0
0
0
2
0
0
3
2
2
1
0
4
2
0
0
0
5
3
0
2
0
4
2
1
2
4
0
1
2
3
4
1
1
0
0
0
0
2
2
0
0
0
0
0
5
0
2
0
3
4
0
0
0
4
0
1
0
0
5
0
0
0
3
0
4
4
0
0
0
0
3
2
3
0
0
1
3
3
0
2
0
0
3
1
0
4
0
1
5
0
2
1
0
4
0
0
3
1
4
0
2
1
1
1
1
4
1
1
5
0
3
1
0
0
0
0
0
4
2
1
0
0
0
3
3
4
1
0
5
4
2
0
3
4
4
4
4
3
0
4
3
0
0
1
4
5
1
0
4
1
0
0
0
1
2
2
4
3
5
0
4
0
1
0
5
0
0
3
0
4
3
0
0
4
2
1
0
3
1
4
3
2
0
0
0
0
0
4
0
4
0
0
0
3
1
1
1
0
3
2
2
4
5
3
0
5
3
4
2
0
3
0
0
1
0
1
2
0
4
0
3
4
0
1
4
2
0
0
0
0
0
5
2
0
0
0
4
2
3
0
0
2
0
0
0
3
3
0
0
0
0
0
5
4
0
4
2
2
1
0
3
1
0
0
1
5
4
1
0
0
4
1
0
0
0
3
1
3
0
2
0
4
0
4
1
2
0
0
0
0
2
2
4
3
0
2
0
5
0
0
2
1
3
0
0
1
0
0
3
0
0
3
0
0
4
0
2
0
0
1
2
2
2
0
2
0
5
1
3
1
0
0
0
1
0
4
0
5
5
0
0
2
2
0
3
0
1
5
0
3
3
0
2
0
3
1
0
1
5
0
0
4
3
1
1
3
3
0
0
3
0
0
3
0
0
1
0
0
3
4
0
4
0
0
0
0
0
0
0
0
5
5
0
0
3
3
0
3
2
0
3
2
0
2
0
2
2
0
2
0
0
4
0
0
0
1
5
2
0
0
0
1
2
1
1
0
4
2
1
0
4
4
4
0
0
3
0
3
2
0
2
5
5
1
2
5
1
2
3
2
2
0
4
4
0
3
3
0
0
0
2
1
1
4
0
1
0
0
0
1
0
5
0
0
2
0
0
0
0
2
2
1
0
4
0
4
0
0
3
2
0
0
2
0
5
2
0
2
3
5
5
2
4
0
0
0
2
0
1
3
2
0
3
0
2
0
0
0
5
2
0
0
5
5
0
0
0
3
0
0
4
5
3
4
0
0
5
0
0
4
4
3
5
2
5
3
3
2
3
0
2
2
0
0
1
0
2
2
3
2
0
0
2
1
5
0
3
0
0
2
3
5
0
2
0
4
0
3
2
0
3
5
3
4
2
0
0
0
3
4
3
0
0
0
4
4
0
5
0
3
2
0
2
2
0
4
2
2
3
0
3
1
5
3
2
4
3
2
1
0
4
4
5
3
5
5
2
5
5
1
2
0
0
0
0
0
0
2
0
3
0
0
0
4
3
3
4
5
5
0
2
5
0
5
0
0
2
0
0
0
1
0
0
0
5
3
3
0
0
3
4
0
4
0
1
0
0
4
3
2
1
0
4
0
3
0
0
0
0
0
1
0
1
0
0
4
0
3
3
0
2
0
3
1
3
0
0
0
1
1
0
0
0
0
3
0
5
2
0
0
3
1
0
2
1
3
0
0
3
0
1
3
1
1
3
0
0
4
3
2
5
0
5
0
3
0
0
0
0
0
0
2
5
0
3
3
0
5
2
4
3
2
5
0
3
3
1
0
0
0
0
3
2
1
4
0
3
0
0
3
4
0
0
0
0
3
2
1
5
2
3
0
1
0
3
4
0
3
5
5
1
4
0
0
2
2
5
1
0
2
2
1
4
0
2
4
3
0
0
3
0
1
0
0
4
2
2
0
0
0
1
1
3
1
2
2
3
3
4
2
4
0
0
2
0
1
4
3
3
3
0
3
1
3
5
0
1
1
3
0
5
2
0
1
0
4
2
0
0
3
2
3
5
1
3
0
0
0
3
0
0
4
3
2
1
1
5
2
1
2
3
2
0
0
1
0
2
2
0
3
3
5
4
1
0
4
3
3
0
0
5
0
3
4
3
0
3
1
4
1
3
4
0
1
4
0
4
1
0
3
0
0
0
5
0
0
2
0
4
2
0
4
0
4
1
1
0
0
2
0
0
0
0
5
2
2
0
0
0
4
2
5
0
0
3
0
0
0
0
0
0
4
1
0
2
0
0
3
3
0
1
2
1
3
0
3
1
2
5
1
0
4
1
0
1
0
0
0
0
2
0
0
0
2
2
4
0
2
0
1
3
5
5
0
3
4
0
0
0
3
1
1
2
0
1
0
0
4
0
4
4
0
5
0
1
0
0
0
0
4
0
2
3
3
0
5
2
2
2
0
3
3
4
3
0
0
0
0
1
0
0
0
4
0
2
1
2
0
1
2
4
0
3
0
0
1
3
4
5
0
2
3
4
5
0
2
0
0
0
4
0
1
2
5
4
2
0
3
5
0
0
0
0
0
5
0
1
4
0
0
2
0
0
4
3
0
1
3
0
2
5
3
4
1
1
0
0
5
4
3
1
0
0
0
5
0
0
3
0
4
0
0
0
4
5
3
3
0
0
1
4
4
2
0
0
2
0
2
0
3
1
0
0
3
0
3
3
3
0
0
2
2
3
1
3
1
0
1
0
2
5
3
0
3
2
3
0
1
4
0
2
1
5
3
2
3
0
0
3
0
0
0
2
1
2
5
4
0
2
0
0
0
4
0
0
4
3
0
0
0
4
4
0
1
4
2
2
4
0
0
0
0
0
5
0
5
3
0
0
0
3
0
0
4
4
2
2
2
4
0
1
0
0
4
2
0
3
2
2
0
5
0
3
3
0
0
1
0
2
0
5
3
2
0
0
3
0
0
0
2
0
0
0
0
1
0
4
1
0
0
3
1
0
0
0
3
0
3
0
5
3
0
0
5
0
1
4
0
1
0
0
3
3
4
2
0
2
0
0
0
4
2
2
0
2
1
0
1
4
3
0
4
3
0
0
5
0
0
0
0
1
0
0
1
5
2
0
1
0
0
0
2
4
1
2
0
0
0
5
4
2
2
0
0
1
5
0
2
3
3
5
0
3
0
3
0
0
0
0
5
0
3
0
0
0
1
0
0
0
0
3
2
3
1
2
0
0
2
0
1
2
3
0
1
0
0
0
0
2
0
0
0
3
5
2
0
0
5
0
0
0
0
3
4
3
0
0
4
2
0
0
0
0
3
5
2
3
0
0
0
0
3
0
0
0
0
3
3
0
0
0
1
3
5
0
3
3
1
0
0
5
4
0
1
2
3
0
3
0
5
1
0
2
0
2
4
2
2
4
0
3
1
0
0
3
1
0
0
0
0
2
0
5
5
2
0
0
0
0
1
1
0
0
0
3
0
3
2
3
0
1
2
0
0
0
0
1
1
3
3
4
4
0
3
0
1
2
3
0
3
0
4
3
0
4
4
1
4
2
0
0
2
4
0
0
0
5
0
5
0
2
2
2
0
0
2
0
0
2
0
4
0
3
2
2
2
5
5
0
4
3
4
0
5
0
3
4
3
4
0
2
3
5
5
2
0
0
5
4
2
1
0
5
0
0
0
2
4
0
0
4
4
3
4
0
2
0
5
2
4
0
0
4
2
0
0
2
0
4
4
0
0
3
0
3
0
0
0
3
2
1
0
4
0
0
3
0
1
3
1
4
0
1
0
3
0
0
0
3
0
3
0
5
0
3
3
0
5
3
0
2
1
3
3
0
2
1
1
4
1
2
0
0
3
0
4
0
1
2
1
0
4
0
3
0
2
4
0
0
0
0
0
0
0
3
2
0
0
2
3
5
0
0
4
4
0
3
0
5
2
3
5
5
0
3
0
1
0
0
0
4
0
0
1
5
0
0
4
1
1
2
1
5
0
0
4
0
0
0
3
0
5
4
3
4
0
2
0
5
3
0
2
0
0
4
4
1
5
0
3
2
0
0
2
0
2
2
2
0
0
0
0
4
0
2
5
0
0
0
3
5
2
0
0
1
0
0
0
1
0
3
3
5
1
5
0
3
1
4
0
0
3
1
4
5
3
0
2
2
0
4
4
1
4
2
0
0
0
5
0
0
4
0
3
3
0
5
0
1
0
0
0
2
0
2
0
2
3
0
0
2
2
5
2
3
1
2
4
0
0
0
0
0
2
2
5
3
0
5
0
3
0
0
1
3
4
5
3
3
5
0
0
1
2
0
0
0
0
0
3
3
2
1
0
2
3
2
3
1
0
4
1
0
5
0
0
4
0
1
0
1
0
2
0
4
0
1
0
4
0
1
5
5
0
0
3
3
3
0
3
5
0
0
0
0
2
2
0
2
1
0
2
0
4
4
4
2
5
0
0
5
0
1
2
0
0
0
0
1
3
3
5
0
0
0
4
1
2
0
1
0
0
0
0
2
0
4
2
3
5
5
0
5
5
4
0
0
2
2
4
3
1
4
5
0
0
2
0
4
0
3
0
2
3
2
0
3
0
3
3
0
3
0
0
0
5
0
0
0
2
4
0
4
1
0
2
0
4
0
2
4
3
2
0
2
3
1
0
2
3
5
4
3
5
3
2
1
1
0
1
0
0
2
1
0
2
2
0
0
0
0
4
1
0
0
4
0
0
1
3
0
0
0
0
0
0
0
4
0
3
0
0
0
1
0
3
3
0
3
2
0
0
5
4
3
0
3
0
0
3
0
3
5
0
4
4
3
4
1
3
3
5
2
3
0
0
5
0
5
4
1
2
0
3
0
3
0
0
4
2
3
0
0
0
4
2
0
4
4
2
3
2
0
0
1
4
2
3
4
4
4
3
0
0
3
4
2
0
0
2
4
0
0
2
0
1
0
5
0
1
2
0
3
3
4
0
0
2
4
3
0
3
0
1
4
1
0
3
4
4
0
1
4
4
3
2
0
5
3
5
0
0
3
2
4
1
5
1
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
4
0
0
3
3
3
2
0
0
1
3
2
0
1
0
2
0
2
0
0
0
3
4
3
1
4
1
2
4
0
0
3
0
2
1
2
0
0
2
5
0
4
0
0
4
3
4
0
1
3
1
3
2
2
2
3
5
5
0
5
0
0
4
0
3
5
0
3
3
3
4
0
3
5
4
0
0
0
0
1
1
2
1
2
3
3
0
0
0
1
0
5
4
1
3
3
0
0
0
0
0
2
0
4
2
0
0
3
0
0
1
0
1
4
1
0
1
2
0
1
1
2
3
4
1
2
2
0
0
0
5
1
0
3
0
0
3
0
0
4
4
0
0
1
0
2
3
0
0
4
0
5
2
1
1
2
0
1
5
4
0
2
4
5
2
0
1
3
0
0
0
0
0
4
5
2
0
0
3
5
3
1
1
2
3
1
4
3
2
2
3
3
0
2
5
3
3
4
2
5
5
0
0
0
0
0
1
0
3
4
2
0
4
1
4
2
1
3
1
0
0
3
1
3
5
2
0
0
0
3
0
0
3
1
3
0
1
4
1
1
0
1
0
0
2
1
0
2
4
1
0
2
4
2
3
3
0
0
0
4
2
0
3
2
4
5
0
0
0
4
0
1
2
2
0
5
3
3
4
5
3
0
0
3
0
2
4
2
3
0
2
0
2
2
3
0
2
0
5
1
0
0
0
0
0
0
0
3
2
3
4
0
0
2
4
4
0
4
4
2
0
0
3
0
2
0
5
2
4
0
0
0
3
4
2
0
0
3
3
3
0
0
5
0
1
3
0
0
3
0
0
2
2
0
2
0
4
5
0
2
1
0
2
4
1
0
0
2
3
0
0
2
0
3
5
4
0
0
0
3
0
0
2
4
1
4
2
5
0
2
0
3
1
0
2
1
2
0
0
0
0
0
5
0
1
0
4
1
1
3
5
2
0
4
3
4
1
2
0
2
0
5
0
5
4
3
0
0
5
2
0
3
0
0
0
2
5
3
3
3
4
3
0
5
1
0
3
0
3
2
0
0
0
5
1
3
1
3
1
0
5
0
1
2
3
3
1
0
0
0
0
0
4
2
0
0
2
5
0
0
0
3
3
0
1
3
0
0
2
1
3
3
0
2
0
2
0
0
3
1
0
0
0
1
0
0
0
1
3
0
0
4
2
1
2
3
0
5
1
0
3
0
0
0
0
0
4
3
4
2
2
0
0
3
0
0
0
0
0
1
3
2
3
2
0
4
0
0
0
5
1
0
0
1
0
2
4
2
0
3
3
2
4
0
4
4
1
1
0
1
2
0
2
3
0
0
4
0
0
1
3
2
0
0
2
0
3
0
0
3
0
0
0
0
4
0
3
0
0
0
4
0
4
0
0
0
0
2
1
0
0
0
3
4
0
3
1
0
0
0
0
0
5
4
0
1
0
0
0
0
4
3
3
5
4
3
4
2
1
2
5
0
2
2
4
0
1
0
0
0
0
3
3
0
0
5
2
0
5
0
0
5
0
2
0
0
2
5
0
0
0
0
0
0
0
5
5
0
5
2
0
4
0
0
5
3
5
4
0
3
2
0
0
2
0
1
0
0
5
3
3
0
5
2
4
3
0
3
1
0
2
2
0
0
5
4
0
1
2
1
4
1
0
0
0
0
2
0
3
1
1
1
0
0
5
0
2
0
0
3
1
1
0
0
4
0
4
1
3
0
0
2
4
0
0
3
3
3
2
0
0
0
5
3
3
5
0
3
1
0
0
0
0
3
2
4
3
0
1
1
1
0
0
0
0
5
5
5
0
0
2
0
0
4
0
1
2
0
0
5
5
5
3
5
4
0
5
2
2
3
5
1
5
4
0
0
3
4
0
0
4
3
1
4
0
3
3
1
4
4
2
0
0
0
0
0
0
5
3
0
0
0
0
5
2
1
4
5
3
2
0
2
3
3
0
3
3
3
2
5
0
2
2
0
2
2
4
2
3
0
1
3
4
5
0
0
0
4
5
1
0
2
0
0
0
0
3
3
5
5
4
0
2
0
0
5
2
3
0
0
0
0
4
3
0
4
0
4
0
0
4
4
3
0
0
2
3
1
1
2
3
3
2
4
0
2
1
0
0
3
2
0
3
4
0
0
0
0
0
0
3
5
0
2
2
1
0
0
1
0
0
4
5
4
0
4
4
0
2
3
1
0
0
0
1
0
1
0
0
1
2
0
3
3
3
2
1
0
3
0
2
3
3
2
0
4
0
0
0
5
0
1
0
0
0
3
0
3
3
0
0
0
0
0
0
1
0
4
0
0
0
0
Answer 12
6%
0
0
0
4
0
0
3
0
1
3
4
5
0
3
3
0
3
1
0
5
2
0
1
0
3
3
3
4
0
0
0
3
0
0
5
4
0
0
3
0
5
5
2
4
4
0
0
3
0
0
0
0
5
0
1
0
5
5
2
2
0
2
0
1
1
0
0
0
0
0
4
2
2
0
4
3
1
0
2
3
4
0
3
0
3
4
0
4
5
2
0
0
3
4
3
0
1
0
1
4
0
1
4
0
3
0
3
3
4
0
3
4
4
2
0
1
0
5
0
3
1
5
0
0
3
3
5
0
2
2
0
1
3
0
4
0
3
0
0
1
2
3
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
5
1
1
3
1
0
4
0
3
4
1
0
0
2
0
3
4
0
5
5
1
0
0
0
3
1
0
0
3
4
3
3
2
4
4
5
3
2
2
1
0
0
4
2
5
0
0
0
0
2
4
1
2
4
2
0
4
3
1
0
0
0
0
3
4
2
0
2
0
4
0
5
0
0
0
3
2
0
0
5
1
3
0
1
4
0
5
0
0
0
1
0
4
0
0
0
2
0
1
5
0
0
0
0
0
5
5
5
0
3
5
2
2
1
0
0
0
0
0
5
2
4
2
0
0
3
0
5
0
0
5
0
0
0
3
3
3
3
0
1
3
4
5
0
1
0
0
4
5
0
2
0
1
1
0
0
0
4
3
0
1
0
0
5
1
0
5
5
3
0
2
0
5
3
3
0
0
1
4
0
3
1
4
0
4
1
2
0
3
0
0
4
3
3
2
4
1
0
0
0
2
5
5
5
2
1
0
1
4
2
0
0
4
5
5
3
0
3
4
1
0
0
0
1
5
0
0
1
2
2
3
3
0
4
0
2
5
0
3
3
3
0
3
1
3
2
0
2
4
4
0
3
0
0
1
4
2
0
0
2
0
3
0
0
0
0
0
2
5
0
2
0
1
3
0
2
0
4
0
0
1
4
3
5
3
0
3
0
0
0
0
4
0
5
0
0
4
0
2
1
0
0
0
1
0
0
3
2
2
5
2
2
0
0
0
0
3
2
0
0
2
0
2
5
0
0
0
0
3
0
1
1
4
0
5
1
3
0
2
3
5
3
2
2
0
4
0
2
2
0
1
0
4
4
0
3
5
3
1
0
5
4
4
2
2
2
1
0
0
3
0
3
4
1
0
3
0
0
5
3
5
1
0
0
0
1
2
3
3
0
0
0
3
5
0
0
3
4
4
1
0
4
0
0
2
0
0
2
1
5
0
0
0
3
0
4
5
0
5
1
0
1
0
0
1
0
3
2
5
0
2
0
0
1
5
0
1
1
0
0
3
4
1
0
0
1
0
0
5
1
0
5
1
0
2
0
0
1
3
3
5
3
2
4
5
2
3
0
0
0
0
2
2
3
3
0
2
0
0
3
2
0
0
2
0
0
4
0
0
3
0
0
0
1
0
0
5
2
3
0
3
3
0
0
1
3
3
5
3
1
0
5
0
0
2
0
3
0
2
0
3
3
1
0
2
2
3
2
3
2
5
4
4
3
0
0
0
0
1
1
0
4
3
1
0
0
4
5
0
0
2
3
2
1
0
0
3
4
1
2
3
5
1
2
1
3
4
4
0
0
0
0
1
2
0
0
3
2
0
5
0
1
0
0
5
2
0
5
2
5
1
0
0
5
0
0
0
3
4
1
4
0
1
4
0
3
2
4
2
0
4
2
1
0
5
0
0
0
3
0
4
0
2
4
3
3
5
5
3
0
1
0
3
3
0
0
4
1
0
0
0
2
1
5
0
3
2
5
0
0
0
0
3
2
4
0
0
0
3
3
1
0
2
3
0
0
0
3
0
5
5
3
1
0
3
0
0
0
2
4
2
1
2
3
1
0
3
0
0
3
4
4
2
5
2
3
3
2
0
3
0
0
4
5
2
3
0
0
4
4
0
0
1
3
2
0
1
0
0
0
4
0
0
0
4
0
0
0
1
1
0
3
3
2
5
0
2
3
1
0
1
3
3
2
1
0
2
1
2
0
3
4
0
2
0
3
0
0
2
4
2
0
0
0
5
0
5
4
0
0
0
0
1
3
3
0
3
2
0
4
0
0
5
0
0
0
3
5
0
2
4
4
3
2
4
3
1
0
5
4
5
4
4
0
0
1
0
5
0
4
4
2
3
0
5
0
0
0
0
1
4
0
0
0
0
0
4
2
2
0
1
0
5
0
2
4
1
3
0
0
1
0
0
4
3
0
0
0
0
3
1
3
0
3
0
2
2
5
0
3
4
5
2
4
4
4
0
0
1
0
0
0
2
4
0
4
1
1
0
3
5
2
0
0
4
1
0
5
0
1
0
0
2
4
0
0
4
5
3
2
2
0
0
0
1
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
5
0
0
2
3
0
3
1
2
1
2
0
1
0
2
4
5
0
5
0
5
0
0
0
2
3
2
0
0
0
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3
0
5
0
3
5
0
1
0
3
5
0
0
0
2
1
3
4
0
2
1
3
3
0
0
0
3
3
4
4
0
5
3
4
3
3
3
5
0
1
0
1
4
3
0
0
0
2
0
3
4
0
0
1
3
2
0
3
2
1
1
0
1
0
5
0
2
5
3
0
4
0
0
0
5
3
0
3
0
2
0
4
2
0
4
2
0
0
0
Answer 13
5%
0
0
3
1
2
0
2
0
2
1
0
3
0
1
2
0
0
2
0
4
2
0
0
4
5
4
4
4
4
0
0
4
0
0
2
5
0
0
1
4
3
0
4
4
2
0
0
2
0
0
0
0
4
0
2
0
4
4
0
1
0
5
0
0
1
0
0
0
0
0
3
1
2
0
5
2
1
0
1
1
2
0
3
0
4
2
5
1
5
0
0
0
1
1
0
0
1
0
1
3
0
0
3
0
2
0
3
2
1
0
2
3
2
1
0
1
0
5
0
3
2
5
0
0
4
3
4
0
1
2
0
1
0
0
4
0
0
0
1
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
1
3
1
0
3
0
0
4
3
2
0
2
0
3
4
0
5
0
1
0
0
0
4
1
0
3
0
0
3
0
2
0
3
5
4
3
0
1
2
0
1
2
0
0
2
0
0
0
2
1
1
1
2
0
0
3
0
0
0
0
0
4
4
3
0
1
0
4
0
5
0
0
0
1
3
0
0
4
3
0
0
1
1
3
1
4
0
0
0
0
2
3
0
0
0
0
0
4
0
4
0
0
0
4
1
0
0
2
3
4
3
1
0
0
0
0
0
5
1
0
3
0
0
0
3
5
0
0
3
0
0
0
3
4
3
3
0
2
4
2
3
0
3
0
0
5
5
0
0
0
1
1
0
3
0
5
3
0
1
1
0
0
2
0
5
3
2
2
2
0
2
4
2
0
0
0
3
0
2
1
2
0
2
1
1
0
3
2
0
4
4
1
1
5
0
0
0
3
2
2
5
0
3
1
0
0
3
3
0
1
0
5
4
4
0
2
3
4
0
1
0
1
3
2
0
1
1
3
0
3
0
3
0
0
3
2
3
0
3
0
3
3
0
0
0
0
4
2
0
1
0
3
1
5
2
0
3
1
2
5
0
0
0
0
0
3
5
0
4
0
1
0
0
2
0
5
0
4
1
4
1
2
3
0
0
0
2
1
0
4
0
1
0
0
3
1
2
4
0
0
0
1
0
0
2
1
1
0
2
4
0
0
0
0
2
2
3
0
1
0
0
1
0
0
4
0
0
0
1
0
1
0
5
3
3
0
2
4
3
2
2
0
0
3
0
1
5
0
3
0
4
4
0
0
0
1
2
0
5
5
3
0
4
1
1
0
0
5
0
2
0
0
0
2
0
0
5
3
5
1
0
0
0
5
3
3
2
2
0
0
3
4
0
0
1
4
3
1
0
4
0
0
3
0
0
3
0
0
0
0
0
4
0
4
3
0
3
0
0
4
0
0
0
0
1
5
5
0
1
0
0
2
5
3
1
4
5
3
1
5
0
0
0
5
2
0
5
1
2
2
1
0
1
0
0
5
3
3
1
0
4
1
3
1
4
0
4
0
2
0
1
2
0
0
2
0
0
0
0
0
2
3
5
0
4
0
0
3
0
0
0
3
0
0
4
2
4
0
1
0
0
0
0
3
0
1
2
0
0
4
0
0
2
0
1
0
1
0
2
0
4
0
1
2
5
0
3
0
0
0
5
3
0
3
0
0
0
0
0
3
5
1
1
0
2
1
0
2
3
1
1
0
0
0
2
3
0
1
1
5
1
2
1
2
1
2
0
0
0
0
1
2
0
0
0
0
0
5
0
3
0
0
1
5
0
0
0
4
1
0
0
5
0
0
0
1
0
2
4
0
0
4
0
0
2
4
0
0
1
1
0
0
5
0
0
0
2
0
2
0
2
3
0
2
3
5
4
0
0
1
1
0
0
0
1
1
1
0
0
2
1
3
0
2
1
0
0
0
0
0
1
2
2
0
0
0
3
1
0
0
1
3
5
1
0
3
0
5
5
3
1
0
3
0
0
0
2
3
3
5
0
4
2
0
3
3
1
2
4
0
2
5
0
2
0
2
5
3
1
5
3
5
2
2
0
0
3
3
0
3
2
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
4
1
2
2
1
0
1
2
1
0
0
3
3
1
1
3
1
3
4
0
3
3
0
0
0
1
0
0
2
4
2
0
0
0
0
5
5
4
1
5
0
0
1
1
0
0
2
0
0
0
0
0
3
0
0
0
2
3
0
0
3
2
3
1
2
4
3
0
0
4
5
2
5
0
0
2
1
0
0
0
2
3
3
0
2
0
0
0
5
5
1
0
0
0
0
0
1
5
1
0
1
0
3
0
0
4
4
0
0
0
0
0
0
4
5
0
2
0
0
2
3
2
0
0
1
1
2
1
0
1
3
2
0
3
4
2
0
0
0
0
4
0
2
4
3
3
1
1
0
2
4
3
0
0
3
1
0
5
0
1
0
0
0
3
0
1
4
2
1
3
2
0
0
0
0
0
0
4
0
0
1
0
1
0
1
0
0
3
0
0
0
0
0
0
0
3
5
0
3
3
0
0
1
2
5
1
2
3
0
0
2
3
2
0
0
2
5
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
3
0
3
0
4
3
2
0
2
0
3
4
0
3
3
3
0
3
3
0
2
1
2
0
3
2
0
0
3
0
0
0
0
1
0
1
3
3
0
2
0
0
0
1
0
0
5
4
0
0
0
0
3
4
4
2
3
3
3
0
3
5
1
0
4
0
3
2
0
3
3
3
4
0
0
0
0
0
0
1
0
1
2
3
2
2
0
1
0
2
0
2
1
0
0
3
0
0
4
0
0
2
0
1
0
4
5
0
2
4
0
5
1
0
1
4
0
2
5
5
1
1
0
5
2
0
2
0
1
0
3
0
0
0
0
2
1
3
0
0
0
0
1
4
1
0
0
0
2
0
0
2
0
1
5
5
3
1
1
0
0
2
3
5
2
2
0
0
4
0
1
1
3
3
0
4
2
0
1
0
1
2
4
4
4
2
5
3
3
3
1
3
0
4
5
0
3
0
0
1
2
2
1
2
2
2
2
0
0
2
4
2
0
3
0
0
2
2
4
3
4
0
0
3
3
0
3
0
0
1
1
4
0
1
4
0
0
0
1
3
5
5
2
5
1
2
2
2
0
0
0
4
1
5
5
2
0
1
0
0
4
0
0
5
0
0
0
0
0
0
1
2
0
4
0
4
0
1
2
0
0
0
0
1
2
0
0
0
0
2
3
0
0
3
1
0
0
1
1
0
0
2
1
1
4
2
1
4
0
1
1
5
2
3
0
5
0
5
0
3
5
5
5
0
3
5
0
4
2
0
1
0
3
3
0
5
0
1
2
0
0
0
0
0
5
1
3
0
0
0
0
0
1
3
0
0
0
0
0
1
2
5
0
3
0
5
3
4
2
0
2
5
4
2
1
0
0
5
1
4
1
0
3
0
1
1
3
1
1
1
1
0
0
0
2
0
0
2
3
0
4
0
0
1
0
2
4
3
1
3
1
4
1
0
0
0
2
0
4
3
1
1
1
0
1
2
4
3
0
1
1
4
0
4
0
0
5
0
0
4
0
0
3
0
4
2
5
3
3
5
3
5
0
0
5
3
0
3
4
5
0
3
3
1
0
0
0
4
0
0
2
4
1
4
5
4
0
0
2
5
0
3
0
0
0
0
0
1
0
2
2
2
0
1
0
1
1
4
0
2
3
0
3
0
0
0
4
0
0
0
0
0
0
0
3
4
0
3
0
0
0
0
1
0
0
0
0
2
2
0
3
0
5
2
0
0
1
4
0
0
0
0
0
0
4
1
0
2
0
0
1
4
0
4
3
0
3
0
3
2
2
0
2
0
4
3
0
3
0
0
0
1
3
0
0
2
1
0
3
0
3
0
3
0
1
4
0
1
4
0
0
0
3
0
4
4
1
2
0
2
5
0
0
5
0
0
0
2
0
2
2
0
2
0
3
0
3
0
5
0
0
2
0
0
5
1
4
0
1
0
0
1
2
0
0
3
0
1
0
3
0
0
2
4
0
3
2
0
0
5
4
5
0
0
3
0
4
5
4
0
0
5
4
0
3
1
2
3
5
4
4
3
0
0
0
0
0
3
0
2
1
0
0
2
0
0
3
2
0
0
4
0
1
1
1
0
2
2
0
0
1
0
0
0
0
5
0
0
0
0
3
1
3
0
0
0
0
0
2
2
0
0
0
0
2
1
0
1
1
0
4
0
1
2
0
0
5
0
2
0
1
0
0
2
2
0
0
0
0
0
1
3
2
0
3
0
1
5
1
0
2
2
0
4
1
0
1
0
5
0
0
1
3
5
5
3
0
3
5
0
0
5
0
0
0
2
0
0
3
3
0
0
0
4
2
0
3
0
2
5
1
0
0
0
0
0
0
2
1
3
4
0
0
1
0
2
2
2
3
1
2
2
1
1
0
3
1
0
0
0
4
2
0
3
5
4
5
0
0
3
0
4
0
1
4
0
2
0
3
0
0
0
0
4
0
0
0
0
0
4
2
0
3
0
2
0
0
0
2
0
1
4
5
2
0
0
1
0
4
3
0
3
0
0
1
2
2
3
0
3
0
0
0
2
1
1
0
2
0
0
1
1
2
5
0
3
0
0
0
0
1
0
4
2
0
4
0
4
1
0
1
0
0
0
2
5
4
4
0
0
0
0
0
1
4
0
0
0
3
0
1
1
3
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
5
3
2
0
0
0
0
2
1
1
0
2
0
0
3
0
2
1
0
0
2
2
3
0
0
5
5
2
0
0
4
2
1
0
0
4
0
4
0
0
2
3
3
0
2
0
0
0
3
0
0
0
0
0
2
5
0
0
0
3
3
0
0
3
1
0
0
0
1
1
0
1
1
0
0
3
0
3
3
0
2
1
0
3
1
3
4
0
4
4
0
0
4
4
0
0
5
0
0
0
5
0
0
0
0
3
0
0
5
0
0
0
0
2
2
4
2
0
3
4
0
0
0
0
0
0
1
0
0
3
0
2
0
1
2
2
0
2
0
5
5
0
3
3
1
3
0
0
0
3
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
5
2
2
2
2
5
5
5
0
2
2
1
0
3
0
3
4
4
0
0
3
5
2
3
1
0
0
1
2
0
3
0
3
0
0
0
2
3
0
0
3
0
3
1
0
3
0
3
0
4
0
0
2
3
2
0
0
0
0
4
0
0
0
0
0
4
0
3
1
2
0
0
1
0
0
1
0
3
5
1
5
0
2
0
0
0
1
0
4
0
4
1
1
0
5
3
0
2
0
0
4
2
0
0
0
3
4
0
3
5
2
0
0
1
4
5
0
0
4
1
0
3
0
3
0
5
3
0
0
0
0
0
0
0
4
2
0
4
1
1
4
0
0
0
3
0
4
3
3
0
0
0
2
0
5
1
0
0
0
0
5
0
0
0
3
0
0
4
3
0
3
4
0
0
1
1
4
0
0
1
4
2
2
4
5
0
2
5
5
5
0
5
0
0
5
3
0
3
4
0
4
0
2
2
0
1
2
0
2
1
4
5
3
0
1
3
0
2
0
2
1
3
0
0
3
0
3
0
1
0
3
0
4
3
3
0
2
1
2
0
0
2
0
2
0
3
0
4
1
0
3
3
1
4
1
0
0
0
3
4
0
2
5
1
2
0
5
0
1
0
4
0
0
2
2
0
0
4
3
4
1
3
0
5
0
3
1
0
0
0
0
5
0
0
2
0
0
3
5
0
2
0
3
0
3
4
4
4
2
4
0
0
2
0
0
0
5
0
0
4
2
1
2
0
3
0
1
0
4
3
5
3
0
3
4
4
2
5
1
0
2
1
0
0
0
0
0
0
4
2
1
2
3
1
0
4
4
4
0
2
3
0
0
0
0
0
1
0
3
5
0
4
0
4
4
3
0
5
0
0
5
0
1
4
0
0
0
4
1
3
3
3
0
0
4
3
0
2
5
1
4
0
1
0
2
0
0
0
5
0
1
0
2
2
4
0
0
5
4
4
2
0
0
5
0
0
5
0
5
2
2
0
0
2
2
0
4
0
3
4
0
5
0
1
0
1
0
0
1
5
3
0
0
2
3
0
3
1
0
0
1
5
0
0
2
0
4
0
0
5
0
0
5
4
1
0
2
0
0
0
0
0
4
1
0
0
2
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
3
2
3
0
0
0
0
0
4
1
1
0
3
1
3
2
0
2
3
5
0
3
0
1
5
0
0
5
0
3
0
0
0
4
0
0
3
3
4
4
0
0
3
0
2
3
0
3
3
1
3
3
0
0
4
4
5
1
0
1
0
0
4
2
0
3
0
1
2
0
2
0
0
2
0
1
1
0
0
0
3
3
0
0
0
0
3
0
0
0
0
0
0
0
0
3
1
1
0
3
3
2
2
4
2
2
0
5
0
0
3
0
5
2
1
0
4
0
0
0
1
0
4
2
0
0
0
1
0
5
0
0
2
0
2
0
0
0
0
2
0
0
3
4
0
4
4
2
4
1
0
0
0
2
1
0
0
0
4
0
0
0
0
0
0
2
0
3
3
1
4
0
3
4
5
0
1
0
0
0
0
1
0
0
3
0
1
2
3
0
1
1
1
0
5
3
4
4
2
5
5
2
0
0
0
0
0
2
0
0
1
3
3
1
4
2
4
0
0
0
0
0
0
5
0
0
3
1
2
0
2
3
1
0
5
3
3
5
4
0
1
0
5
0
2
4
3
4
1
2
0
0
0
5
0
1
5
0
0
3
5
0
0
0
0
2
5
1
0
0
0
0
0
2
0
3
0
5
5
0
0
3
5
0
0
0
3
4
4
1
0
0
2
0
3
3
0
5
2
2
1
1
3
0
1
5
0
0
0
3
1
1
0
4
0
0
3
5
4
0
0
4
5
3
1
0
5
3
1
4
1
3
0
3
3
3
0
4
3
3
2
1
5
0
4
0
1
0
4
1
0
1
4
3
0
2
1
2
1
0
5
5
0
0
1
3
1
5
0
0
0
0
4
0
0
3
1
1
0
3
3
2
3
0
5
2
0
3
3
3
0
4
1
2
3
4
3
0
4
0
0
0
3
2
0
5
1
5
4
0
0
0
3
3
0
0
0
0
0
3
3
4
0
4
0
0
4
0
1
1
0
3
0
4
1
3
3
2
0
3
0
0
3
0
1
0
1
0
0
0
2
0
2
1
3
0
1
4
2
0
0
4
3
0
0
3
0
3
0
0
4
1
0
0
0
2
4
0
3
0
0
0
3
5
0
2
0
0
5
0
4
5
0
0
3
4
2
1
0
4
5
0
1
1
2
3
3
0
0
0
4
4
0
3
1
5
1
0
5
0
1
0
3
0
5
2
0
1
3
0
0
3
2
0
0
1
0
0
1
0
0
0
4
3
0
4
0
3
0
3
5
0
5
0
3
4
3
0
1
0
1
0
0
3
0
0
4
5
1
0
0
3
1
0
2
0
0
0
5
2
0
0
0
5
5
0
1
1
0
4
2
3
0
0
0
0
0
1
1
4
0
5
0
3
0
3
2
0
2
4
0
0
3
0
4
0
5
4
0
5
3
0
0
0
5
3
0
0
0
0
0
1
1
0
4
0
1
0
2
0
0
1
1
0
1
5
0
0
0
0
0
0
0
0
2
2
1
2
1
2
0
5
2
2
0
0
0
0
0
1
3
1
2
2
1
0
1
0
1
0
0
0
0
2
1
3
4
3
3
4
0
2
5
1
5
0
1
0
1
2
3
0
2
3
3
5
0
2
0
3
3
0
0
3
0
4
3
2
0
3
0
0
3
3
0
0
0
0
0
5
0
0
4
0
0
0
0
0
5
2
3
0
2
0
0
5
0
1
0
0
0
0
1
3
0
2
4
4
2
4
0
0
0
0
0
4
3
1
4
1
0
0
3
5
2
5
0
0
4
3
3
3
5
2
4
2
1
3
0
0
0
0
0
0
0
3
0
1
1
5
0
1
0
0
0
0
2
0
0
1
5
4
0
0
0
5
0
0
3
5
0
1
3
0
4
0
0
0
3
2
3
0
0
2
3
0
3
0
0
0
4
4
3
0
0
5
4
5
3
0
3
2
2
3
4
0
0
4
3
1
2
4
2
3
1
0
0
4
0
0
0
3
1
3
3
0
0
3
0
2
5
0
0
1
1
0
0
0
0
4
3
4
2
0
0
2
4
0
0
3
0
2
5
0
0
2
0
3
5
0
0
2
0
0
0
4
0
1
1
4
0
0
1
3
0
0
0
0
4
4
3
0
0
1
0
0
3
3
2
1
0
0
0
4
1
1
4
4
0
3
3
4
3
3
2
4
5
0
0
3
2
0
0
3
2
0
4
0
0
0
2
1
2
4
0
5
2
0
3
0
0
0
4
0
0
4
0
0
0
4
5
5
5
0
1
3
2
0
3
2
4
1
0
0
0
1
0
0
1
1
0
2
0
1
3
5
5
3
0
5
5
3
4
0
1
3
0
0
0
0
3
5
4
3
0
4
0
0
4
0
2
4
0
0
4
3
2
0
3
0
1
0
3
2
3
2
0
0
5
1
3
1
3
2
2
2
3
0
3
0
0
4
3
0
3
3
5
0
0
1
0
1
0
2
0
3
1
1
2
0
0
0
3
3
3
2
0
0
3
3
3
2
4
1
0
1
0
1
2
3
0
0
0
1
0
1
3
0
0
0
0
3
0
1
2
4
1
0
4
0
2
0
1
0
3
0
0
0
0
0
5
2
0
0
0
5
0
0
2
0
4
0
0
0
0
Answer 14
6%
2
5
0
5
0
0
4
2
1
0
0
0
0
1
2
0
5
4
0
5
1
0
1
0
5
5
5
5
5
0
0
0
0
0
4
5
0
0
1
0
5
0
1
2
0
3
0
3
3
0
0
4
2
0
1
0
0
1
2
2
0
4
0
3
3
0
0
0
0
0
0
0
1
0
0
4
0
3
1
2
4
0
3
0
4
5
0
3
5
0
0
0
3
0
3
0
0
5
0
4
0
0
3
0
0
0
5
1
2
0
0
4
1
0
0
3
0
5
3
2
2
4
4
0
3
5
4
0
1
2
0
0
1
1
3
0
0
0
1
0
3
5
5
0
2
1
0
3
1
0
0
2
1
5
0
0
2
2
1
5
1
0
1
1
0
3
2
1
3
0
4
2
3
0
5
0
4
2
0
2
0
3
3
0
0
3
1
5
2
2
5
4
0
1
0
1
0
4
1
0
1
0
0
5
1
4
1
4
1
0
3
0
0
3
5
3
5
1
4
0
0
0
0
5
4
4
4
2
2
3
0
3
5
0
0
2
1
2
0
0
5
1
2
3
2
0
0
0
0
0
0
1
0
2
3
0
0
3
0
3
5
5
0
0
0
0
0
5
0
0
5
5
0
0
1
0
1
0
0
0
5
3
4
4
4
0
3
4
3
0
0
5
0
0
0
4
3
0
3
0
1
5
3
3
0
5
0
0
2
3
0
0
0
1
1
0
4
0
5
2
3
1
0
0
5
5
0
1
0
4
2
5
0
1
1
3
0
0
4
2
0
2
1
4
0
1
1
2
0
4
0
0
0
5
4
0
5
0
0
0
1
2
5
5
4
3
3
0
4
3
3
0
2
5
4
5
3
0
1
5
4
0
1
1
1
5
4
0
4
0
0
1
0
0
0
0
1
1
1
2
3
3
0
2
0
3
5
0
3
4
4
0
3
3
1
0
1
0
0
4
4
0
5
3
1
0
5
4
3
5
2
3
1
1
2
1
4
0
0
2
0
3
4
4
0
4
0
3
0
3
0
0
0
0
1
2
0
2
0
2
3
2
2
0
2
0
0
3
1
1
2
3
3
2
0
3
0
3
1
1
0
4
1
0
5
0
0
2
0
0
0
1
0
5
0
5
0
3
0
3
5
3
3
2
0
0
3
0
3
2
0
0
2
3
0
0
0
5
3
0
0
0
4
5
5
3
0
3
0
0
5
0
2
5
1
3
4
1
0
3
4
2
3
0
0
0
1
0
3
1
0
0
0
4
0
0
0
5
4
3
1
0
1
0
2
4
0
0
1
0
0
3
0
0
1
4
5
4
4
4
0
0
4
0
0
0
5
2
1
5
0
1
3
3
1
2
0
4
2
0
0
0
4
1
0
4
5
2
0
3
0
2
4
1
0
3
0
4
0
5
0
5
1
1
2
5
1
2
0
2
0
0
3
3
2
0
2
2
3
0
0
4
3
0
4
5
0
3
0
0
3
0
1
0
0
3
0
0
4
4
0
4
4
0
3
0
5
3
1
3
0
0
5
2
0
0
0
4
0
2
2
1
4
2
0
1
1
0
0
2
0
3
4
4
2
5
0
0
0
2
2
3
4
2
1
4
4
1
2
0
2
0
4
1
1
0
0
2
5
1
3
1
0
0
3
4
0
1
0
0
1
0
0
1
4
0
0
0
3
0
3
0
5
0
0
5
4
0
0
5
5
0
0
0
5
0
3
0
3
0
1
4
0
1
0
0
0
3
3
2
0
1
2
3
0
3
0
0
2
3
0
4
0
2
2
0
3
2
0
5
0
1
0
0
3
3
0
4
3
0
0
0
2
2
3
0
2
3
4
0
0
1
0
3
1
5
0
0
5
3
3
1
2
3
3
2
0
0
2
4
5
4
5
1
0
2
2
1
1
0
5
4
2
2
3
2
0
3
4
4
5
3
2
3
5
0
2
1
2
0
3
2
5
2
5
2
2
0
1
3
3
0
0
1
5
2
0
0
0
0
0
3
0
0
0
3
0
0
0
5
0
0
1
3
3
5
0
2
2
0
0
5
4
2
2
1
0
0
4
4
0
0
3
5
0
0
2
0
0
2
3
3
0
2
0
2
0
5
2
0
0
0
3
1
2
3
0
3
0
0
0
0
0
5
0
0
0
0
0
5
0
2
4
5
2
3
1
1
0
5
1
0
3
1
2
0
4
1
0
3
0
1
1
3
5
2
0
0
0
0
4
1
3
4
0
0
1
5
4
0
0
1
0
0
0
2
2
4
3
0
0
2
0
5
3
1
0
3
0
0
2
0
3
5
0
3
1
3
3
0
1
1
5
3
4
4
5
0
0
0
0
5
0
5
5
0
0
1
0
3
3
0
1
0
0
5
3
0
5
3
1
0
0
5
2
0
0
5
0
3
4
2
0
0
0
1
4
0
5
0
0
1
0
3
4
3
0
0
1
0
0
0
0
0
1
0
4
4
0
5
5
0
0
1
1
0
1
3
5
4
0
3
1
3
2
0
0
4
0
1
0
4
1
2
0
0
0
2
4
2
0
0
1
0
0
0
4
5
3
5
0
2
0
2
0
0
5
2
2
5
0
3
0
3
2
3
0
3
2
0
0
4
1
0
2
0
3
0
1
4
0
0
1
0
0
3
3
1
2
0
3
0
0
0
0
1
2
3
0
0
4
2
0
5
5
2
0
5
0
0
0
0
0
1
4
5
0
0
3
0
1
0
4
0
1
2
1
4
1
2
5
5
1
0
1
0
0
2
2
0
5
1
0
3
0
0
1
0
2
5
0
4
2
0
5
1
3
5
3
0
4
0
3
5
0
3
5
0
0
1
3
5
0
2
0
5
0
2
3
3
1
0
5
5
0
2
2
0
0
0
0
1
2
0
3
0
3
0
3
4
3
3
0
0
3
3
5
3
0
0
1
1
5
2
0
2
4
0
0
1
0
4
2
1
3
0
4
1
3
3
3
2
3
0
0
5
5
3
0
4
0
0
4
1
3
0
0
2
0
4
0
0
0
2
4
1
0
0
0
2
2
5
1
2
0
0
5
5
5
5
0
0
1
0
0
0
2
0
0
0
1
2
5
0
0
4
4
1
5
0
3
5
0
5
5
5
5
4
2
1
3
0
5
0
0
0
1
0
1
3
5
0
4
0
1
0
2
0
1
3
2
3
3
0
1
0
0
0
0
0
0
0
5
1
3
0
3
3
5
2
1
3
4
3
3
0
2
4
0
2
4
0
0
3
5
0
5
2
5
3
5
0
2
0
0
0
0
2
5
0
2
2
0
4
0
4
3
0
4
1
1
4
0
5
1
0
0
5
0
1
2
0
4
0
0
5
5
0
2
0
4
0
2
4
5
3
4
2
4
0
1
1
0
3
2
4
3
3
0
3
5
2
5
1
0
4
1
5
1
0
3
3
3
0
0
1
0
2
0
0
3
5
1
1
0
4
2
1
5
3
0
1
0
4
2
2
0
0
5
3
0
4
3
2
4
1
0
4
0
0
2
5
3
4
3
5
3
0
5
5
0
0
5
0
0
1
2
3
2
1
4
0
3
5
5
0
0
5
3
4
3
4
5
0
4
0
3
0
3
2
1
0
1
5
0
2
4
2
4
3
0
2
4
0
0
0
5
0
5
3
1
0
4
0
3
3
1
0
0
3
0
0
3
5
4
1
0
2
1
4
0
0
1
2
3
0
0
4
4
0
3
2
0
0
0
1
0
0
0
0
3
2
0
5
0
0
3
5
2
0
4
0
0
0
2
0
0
2
3
0
0
0
0
4
2
1
1
5
0
4
0
3
3
4
0
4
0
3
1
0
2
0
0
1
0
1
0
0
3
4
3
2
5
3
2
2
0
1
5
3
0
5
3
0
0
3
3
5
2
2
1
0
0
1
0
0
2
5
0
0
3
0
3
5
0
5
0
4
2
1
0
4
4
0
2
0
0
5
4
5
0
3
0
2
3
0
0
1
0
0
4
1
5
0
3
3
3
0
5
0
0
1
2
5
4
0
2
5
0
3
0
1
2
0
0
5
0
4
3
1
1
3
4
1
3
0
4
3
5
4
4
0
4
3
0
0
2
2
0
2
3
0
1
3
0
1
1
1
0
3
1
4
0
3
2
5
1
0
3
0
0
3
0
3
1
4
2
4
2
4
2
2
4
0
0
0
3
3
3
0
0
2
0
2
0
0
0
0
0
4
0
1
1
2
4
2
4
1
0
0
1
5
0
1
1
4
5
4
2
1
2
3
5
0
3
0
3
1
0
0
0
5
0
5
0
0
0
5
2
1
2
0
1
0
3
0
0
0
3
0
0
4
2
0
3
0
5
4
2
4
0
2
5
0
0
0
0
3
0
0
3
2
4
0
0
0
2
4
1
3
1
1
0
4
5
1
3
0
2
3
3
3
4
5
2
0
0
0
4
5
0
4
5
0
5
0
3
4
0
0
0
3
0
0
2
2
4
3
0
0
4
0
1
3
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
0
0
2
2
1
4
0
4
5
1
4
3
0
3
0
0
0
3
1
3
5
0
4
0
3
1
1
0
5
5
0
0
0
0
2
1
4
3
0
0
0
5
0
0
0
0
0
0
2
2
4
2
0
0
0
0
0
4
5
1
0
2
2
0
1
4
4
4
0
4
0
3
0
3
0
0
1
0
0
0
0
0
0
4
0
0
1
5
0
3
2
3
0
0
2
0
5
3
1
0
2
0
0
2
0
2
2
0
0
3
1
5
0
0
5
4
2
0
0
5
4
1
0
0
4
0
5
0
0
2
4
2
5
1
0
4
3
0
1
3
0
0
0
3
3
0
0
0
4
3
0
0
4
1
1
0
1
3
2
3
3
2
0
5
4
0
5
4
0
0
1
2
2
5
4
3
0
1
1
0
4
5
4
0
0
5
0
5
0
5
0
0
0
2
4
0
1
3
0
3
2
1
5
1
2
1
0
0
3
0
0
5
0
1
2
0
0
0
4
0
3
0
2
4
3
0
4
4
5
5
3
4
1
5
2
2
0
0
0
3
5
2
4
0
3
0
0
2
0
3
0
0
5
0
3
0
0
3
4
3
4
4
5
4
0
0
3
3
2
0
3
0
2
5
5
3
3
1
3
2
2
4
0
0
1
4
0
4
5
3
0
4
0
3
3
0
0
3
3
3
1
0
2
0
2
0
4
1
0
4
4
0
5
5
0
0
4
0
0
2
0
0
0
0
0
0
5
0
0
2
2
4
3
0
3
1
1
2
0
4
2
4
0
0
0
3
0
4
0
5
0
4
5
0
2
4
3
3
1
0
0
0
1
4
0
5
5
3
0
0
3
0
5
0
0
2
2
0
3
3
4
3
2
3
0
0
0
0
0
5
0
3
5
2
0
1
3
2
1
0
3
5
0
5
4
5
0
0
4
1
0
3
2
3
0
0
0
3
0
5
1
5
0
0
4
5
2
1
4
0
4
0
3
0
2
0
1
1
0
5
1
1
0
2
0
5
3
0
5
5
0
5
0
0
0
4
5
5
0
2
1
0
1
5
3
0
3
0
2
0
0
2
4
0
3
4
2
4
0
0
0
4
0
0
4
1
0
3
4
4
2
3
0
5
1
2
3
0
2
0
2
0
0
0
1
2
0
2
4
4
4
1
3
1
0
5
0
0
4
5
4
0
0
5
4
2
0
2
5
0
4
4
0
1
2
0
0
2
4
0
2
2
1
4
0
0
0
0
0
0
0
2
1
0
0
0
3
2
0
1
0
2
2
3
5
2
3
0
0
0
1
0
2
5
0
0
5
5
4
0
0
3
0
0
2
5
0
5
4
1
4
2
5
3
2
1
0
2
2
0
0
3
1
2
0
4
0
1
3
5
3
0
0
0
0
0
2
2
0
0
0
0
1
1
0
4
3
0
2
4
2
5
1
3
3
0
2
0
0
1
2
0
4
0
1
1
2
2
3
0
0
1
3
2
3
0
2
1
0
0
0
3
0
0
0
5
4
1
0
5
1
4
0
0
5
4
4
5
4
0
5
0
0
3
0
4
3
0
0
0
4
4
3
3
0
4
5
1
3
2
0
0
0
5
0
3
4
3
0
0
5
2
1
0
3
0
0
1
5
3
0
3
2
3
0
0
5
0
0
2
5
1
2
0
0
1
0
0
5
1
3
0
0
1
0
0
0
0
2
0
0
0
4
0
0
1
1
0
0
0
0
3
0
0
0
0
1
5
0
0
3
0
1
0
1
2
0
0
0
2
4
1
0
0
0
0
3
5
2
5
0
4
3
1
5
0
1
1
5
0
2
0
5
0
1
0
5
0
4
0
2
4
5
0
0
4
4
2
4
0
0
5
2
2
4
2
1
5
4
0
0
0
0
3
3
5
0
3
5
1
4
4
1
0
0
5
3
4
0
0
0
0
1
0
3
0
0
1
0
3
3
0
4
0
4
1
2
0
1
0
0
0
0
0
3
1
0
2
3
4
3
1
4
5
1
2
5
0
4
4
1
3
5
1
0
5
3
3
1
0
4
0
2
0
4
0
2
3
5
3
0
4
0
3
3
0
4
0
4
3
2
2
3
0
0
4
2
1
4
0
0
0
2
4
0
1
0
2
1
0
0
0
0
0
2
2
2
0
1
5
0
0
4
3
0
3
1
5
0
0
3
5
0
3
0
5
4
4
0
3
4
1
0
0
3
1
2
3
5
3
0
5
0
0
2
0
0
0
0
3
4
4
2
0
4
4
0
0
0
0
4
0
5
0
0
2
4
1
0
3
1
3
0
5
3
0
3
1
0
4
3
0
1
3
1
2
4
5
5
0
0
0
3
0
1
3
4
0
3
5
0
0
0
4
1
2
0
0
0
4
0
0
5
1
2
3
0
0
3
0
3
2
0
2
0
4
0
1
3
2
0
3
0
5
1
0
4
3
1
2
4
5
5
3
2
4
1
0
5
2
1
0
0
1
0
4
5
4
0
0
4
5
0
1
3
4
2
0
4
3
1
4
4
4
3
0
3
4
3
2
1
2
0
5
0
0
0
2
1
0
1
1
3
4
2
2
2
3
2
5
2
0
0
3
0
2
0
1
5
0
0
0
0
0
4
2
2
5
2
2
2
1
0
5
2
0
0
5
0
0
4
0
0
5
5
3
0
4
4
0
0
4
4
1
5
1
2
5
0
5
0
4
0
4
0
5
0
0
2
5
5
0
0
0
0
3
2
3
2
5
2
0
2
0
4
0
2
1
3
3
0
2
0
0
1
0
0
0
0
1
2
3
3
0
0
4
5
3
0
0
4
1
4
0
3
1
3
0
3
5
3
4
0
0
1
3
0
3
0
2
3
3
0
0
0
1
0
5
0
4
1
0
0
4
3
1
1
0
4
3
0
2
3
0
3
2
3
0
0
2
2
0
0
2
0
3
5
4
4
0
0
4
5
3
1
4
1
3
4
5
0
0
0
0
2
0
0
1
3
0
0
0
2
0
4
0
3
0
5
5
0
5
5
4
0
1
0
4
1
0
0
4
2
0
0
4
4
3
0
0
2
1
2
0
4
0
0
2
3
0
3
0
2
2
0
3
1
0
4
0
3
3
4
0
0
5
0
5
1
4
3
0
4
4
3
4
3
4
1
0
0
5
0
0
0
4
0
2
0
3
2
0
0
4
2
3
0
1
0
2
1
4
0
4
3
0
5
1
5
0
1
1
2
0
5
0
3
0
2
0
0
0
3
5
3
3
3
2
0
3
5
4
2
0
1
1
0
3
4
4
4
4
3
0
0
0
0
0
1
0
0
1
4
3
5
3
0
4
4
0
0
5
0
2
0
2
0
2
1
3
0
3
1
4
5
0
2
0
4
1
0
0
5
3
1
0
0
0
5
3
0
1
1
0
0
4
0
4
4
0
4
3
0
2
0
0
3
0
4
4
0
0
0
0
0
0
4
0
0
0
0
1
0
0
4
4
5
2
2
0
0
0
0
0
3
3
5
3
0
3
0
0
4
4
5
0
0
3
3
5
1
2
5
0
2
1
2
4
0
0
0
0
0
1
5
0
3
3
5
0
0
0
0
3
3
4
0
5
2
5
2
0
0
0
0
3
0
5
5
0
4
3
3
3
0
5
0
2
2
1
0
0
3
3
0
4
2
1
0
5
3
3
0
0
5
2
5
3
0
1
0
0
1
3
0
0
2
1
0
5
1
3
3
1
1
0
0
3
0
0
4
3
3
3
1
0
5
2
1
5
0
3
0
1
0
0
0
0
3
4
1
0
0
0
3
0
5
4
4
0
5
0
0
5
4
0
3
3
0
4
4
4
0
2
0
1
1
2
3
0
2
0
4
0
0
1
0
4
4
3
0
0
0
5
0
4
0
1
5
0
0
0
5
1
1
2
4
0
3
2
1
4
2
1
3
2
0
1
3
3
0
0
5
3
4
3
0
4
0
3
1
4
5
0
4
5
0
0
0
0
0
2
0
0
0
0
2
0
2
4
0
3
0
0
0
4
0
3
3
2
1
0
1
0
1
0
0
1
3
3
3
0
3
3
5
3
3
0
0
2
3
4
0
1
2
4
0
0
0
2
5
3
5
0
1
0
0
5
0
1
4
0
4
2
5
4
5
5
0
2
0
0
0
5
3
0
3
1
4
3
2
3
3
1
3
1
5
4
0
0
3
0
2
0
4
0
0
0
3
0
0
3
2
2
0
1
4
2
0
0
2
5
4
4
4
3
0
3
2
1
2
3
5
3
2
0
1
0
2
0
0
0
0
0
1
1
0
0
2
0
4
5
3
4
3
3
0
3
0
3
2
1
5
3
0
1
0
3
0
2
2
0
4
5
0
1
0
3
0
5
2
4
0
0
Answer 15
5%
0
0
0
0
0
0
3
0
0
0
1
0
0
3
0
0
0
2
1
2
2
0
0
0
4
5
2
2
1
0
0
0
2
3
2
2
0
0
2
0
3
0
2
4
0
3
0
4
0
1
5
0
1
3
0
0
2
1
0
2
0
2
5
3
3
0
0
0
0
3
0
0
4
0
0
0
0
0
1
1
1
0
2
0
2
2
0
0
3
1
0
3
3
0
2
0
0
0
4
5
0
0
2
0
2
0
5
2
1
0
5
1
5
0
0
1
0
0
1
0
0
4
0
0
0
4
2
0
0
3
2
0
0
0
4
4
0
2
0
0
2
2
4
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
4
1
0
0
0
0
3
1
0
1
5
0
1
2
1
4
0
1
0
5
0
2
2
0
1
2
5
3
4
4
0
1
5
2
4
1
1
0
0
3
2
0
0
3
0
0
1
2
0
2
0
1
0
0
0
3
0
0
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0
0
0
0
0
2
1
0
4
0
0
0
2
0
2
2
4
0
0
1
2
0
3
2
1
3
4
3
4
0
5
0
0
0
1
0
0
1
2
0
3
2
0
1
2
0
0
0
0
0
0
5
0
0
2
1
4
0
4
4
4
0
5
2
1
0
4
0
4
4
0
0
1
0
0
2
0
4
0
0
0
2
0
0
3
1
1
2
0
0
0
2
3
0
1
0
0
0
0
0
4
1
0
0
1
0
0
0
0
5
2
0
0
0
0
0
0
3
0
0
2
0
0
4
0
0
1
0
3
2
1
0
0
4
0
0
0
3
3
4
0
4
0
0
3
5
3
0
0
3
3
4
1
0
2
1
0
4
1
1
0
3
2
0
1
1
3
5
5
1
5
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
4
3
0
2
0
0
5
0
1
0
2
0
0
0
5
0
0
1
3
3
5
0
1
0
1
0
5
0
0
4
1
0
4
4
0
0
2
1
0
2
3
0
0
1
3
2
0
2
1
3
5
0
0
0
2
0
1
0
0
0
0
1
1
4
0
0
0
0
1
0
3
1
5
1
0
4
3
3
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
1
1
3
0
3
2
3
4
0
0
3
1
0
0
0
0
2
0
0
3
5
2
0
0
4
4
0
0
0
4
0
1
0
0
5
0
0
5
0
4
2
0
0
1
2
0
3
0
2
3
0
1
2
0
0
4
1
0
0
1
0
0
4
1
5
4
5
5
0
0
0
2
0
1
2
4
1
2
2
2
0
3
2
2
2
5
0
1
3
5
0
0
1
5
5
0
5
3
2
1
0
3
1
3
3
5
3
1
1
3
0
2
0
0
0
3
2
4
0
0
1
2
2
0
0
0
0
1
0
0
5
0
1
3
0
1
1
0
2
0
4
2
4
0
0
0
0
1
0
2
0
0
5
5
2
3
3
3
1
0
0
0
0
4
0
3
5
5
1
0
0
0
0
2
1
0
0
0
0
0
3
4
0
2
1
2
0
1
5
0
3
3
1
3
0
0
2
0
0
0
0
0
0
4
2
1
0
3
0
0
1
2
4
0
0
1
1
0
5
0
3
0
2
2
0
4
0
0
0
0
0
2
0
3
1
2
2
3
0
0
0
0
1
5
0
0
0
2
1
3
0
1
1
5
4
0
0
2
1
1
0
1
4
0
1
2
0
4
1
0
2
3
3
0
4
0
0
0
4
0
3
2
3
0
0
0
3
0
1
0
1
4
0
0
0
0
0
0
4
0
0
2
0
0
3
4
0
1
0
0
0
0
0
0
3
1
0
3
1
0
0
0
1
2
3
0
0
0
4
1
5
1
2
0
4
1
5
4
0
0
0
0
0
1
0
0
3
4
2
2
0
0
1
0
1
4
1
0
1
3
5
0
5
0
0
0
0
4
0
0
5
0
0
1
0
3
1
5
3
4
3
0
1
2
0
4
0
0
0
0
0
2
0
0
0
3
4
4
0
0
0
0
2
4
0
3
5
1
1
1
0
0
4
1
0
0
0
0
0
0
2
3
1
1
0
0
3
4
1
0
0
5
0
0
0
0
0
3
2
1
1
0
0
0
2
0
5
0
4
0
0
5
0
0
5
3
3
3
0
0
1
1
0
0
0
0
1
0
3
0
4
2
2
5
0
2
0
4
4
3
0
0
2
0
0
5
0
3
3
4
4
0
5
1
0
3
2
0
1
0
1
3
2
2
1
5
0
2
3
3
0
2
0
4
0
3
0
1
0
4
2
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
3
5
1
0
1
4
4
3
3
2
1
0
0
0
1
0
0
1
4
0
1
0
1
5
3
3
0
0
0
4
1
0
0
2
0
0
0
0
0
3
5
0
4
0
2
0
0
5
1
1
3
0
0
0
0
1
2
5
0
3
0
0
0
2
2
0
0
0
0
1
2
4
5
1
2
1
0
1
0
0
4
0
2
0
2
0
0
0
4
0
1
0
0
0
2
2
3
0
0
0
3
4
0
2
4
0
0
3
2
3
3
3
3
0
0
0
4
0
3
0
0
0
2
0
2
3
0
0
2
0
0
0
1
3
2
3
4
1
0
4
0
0
3
1
0
0
0
0
0
3
4
0
0
0
0
0
5
1
0
4
3
1
0
0
Answer 16
2%
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
2
0
4
0
0
0
0
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2
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1
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1
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3
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0
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0
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0
0
1
1
1
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0
1
0
0
0
1
3
3
0
2
1
0
0
0
0
0
4
0
1
0
0
0
0
0
1
1
0
0
1
2
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0
0
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1
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1
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2
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0
1
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0
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1
0
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1
1
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0
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1
1
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0
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1
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1
0
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3
1
0
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0
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0
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1
0
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1
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1
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1
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1
1
1
0
1
0
0
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0
2
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5
0
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1
0
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3
2
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4
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1
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1
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1
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0
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4
0
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0
1
1
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1
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1
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1
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1
0
1
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1
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0
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1
0
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2
0
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3
0
0
3
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1
2
0
2
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2
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1
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1
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1
0
1
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1
0
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1
0
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1
4
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1
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0
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1
1
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0
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0
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0
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1
0
0
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0
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0
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0
0
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1
0
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1
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1
0
0
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0
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1
0
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1
0
0
0
1
0
0
0
1
0
3
3
2
0
0
1
0
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0
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0
0
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0
0
0
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4
0
0
5
0
1
0
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3
0
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0
1
2
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2
0
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0
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0
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0
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0
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1
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0
0
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0
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0
3
1
1
0
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0
0
0
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2
0
1
2
0
1
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0
0
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0
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0
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0
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2
4
0
0
1
1
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0
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0
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3
0
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3
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3
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0
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0
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0
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0
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2
2
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4
1
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0
0
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2
0
0
0
0
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0
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0
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1
0
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1
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1
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0
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1
0
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0
0
0
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1
1
0
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1
2
0
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0
0
0
0
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1
1
0
0
3
0
0
0
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0
0
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0
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0
1
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1
0
0
0
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3
3
0
1
0
1
1
0
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0
0
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0
0
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0
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0
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1
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0
0
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0
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0
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2
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0
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0
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0
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1
4
0
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1
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1
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1
1
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1
1
0
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1
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1
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0
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3
1
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3
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3
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ප්රස්ථාරයේ 3933 ප්රති results ල පෙන්වන්න
අපනයනය සඳහා ප්රතිඵලයක් (ඊ-තැපෑල) තෝරන්න
අපනයනය සඳහා ප්රතිඵලයක් (ඊ-තැපෑල) තෝරන්න
මෙම ක්රියාකාරිත්වය ඔබේම VUCA මැතිවරණයෙන් ලබා ගත හැකිය
If you participated in VUCA polls, you can see your results and compare them with the overall polls results, which are constantly growing, in your personal account after purchasing
ගාස්තු «මගේ SDT»
VIDEO
[1] https://twitter.com/wileyprof
[2] https://colinallen.dnsalias.org
[3] https://philpeople.org/profiles/colin-allen
2023.10.13
Fear person qualities project organizational structure RACI responsibility matrix Critical Chain Project Management focus factor Jira empathy leaders boss Germany China Policy Ukraine Russia war volatility uncertainty complexity ambiguity VUCA relocate job problem country reason give up objective key result mathematical psychology MBTI HR metrics standard DEI correlation risk scoring model Game Theory Prisoner's Dilemma
වැලරි කොසෙන්කෝ
නිෂ්පාදන හිමිකරු SaaS SDTEST®
