The Undefeated Team

Easy

A tournament has n teams numbered 0 to n - 1. For every pair of teams we know which one is stronger, recorded in an n × n matrix beats. For i ≠ j, beats[i][j] == 1 means team i is stronger than team j, and 0 means the opposite. The diagonal is all zeros. The champion is the team that no other team is stronger than. A champion is guaranteed to exist. Return its number.

Example 1

beats=[[0, 0, 0], [1, 0, 1], [1, 0, 0]] → 1

Team 1 is stronger than teams 0 and 2, and no one is stronger than team 1.

Example 2

beats=[[0, 1], [0, 0]] → 0

There are only two teams, and team 0 is stronger than team 1.

Constraints

2 ≤ n ≤ 100
beats[i][j] is 0 or 1, and beats[i][i] == 0
For i ≠ j exactly one of beats[i][j] and beats[j][i] is 1
A champion exists

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Topics

Array Matrix

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Input

beats=[[0, 0, 0], [1, 0, 1], [1, 0, 0]]

Expected

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