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The Celebrity Problem
Medium Accuracy: 39.46% Submissions: 59428 Points: 4

A celebrity is a person who is known to all but does not know anyone at a party. If you go to a party of N people, find if there is a celebrity in the party or not.
A square NxN matrix M[][] is used to represent people at the party such that if an element of row i and column j  is set to 1 it means ith person knows jth person. Here M[i][i] will always be 0.
Note: Follow 0 based indexing.

 

Example 1:

Input:
N = 3
M[][] = {{0 1 0},
         {0 0 0}, 
         {0 1 0}}
Output: 1
Explanation: 0th and 2nd person both
know 1. Therefore, 1 is the celebrity. 


Example 2:

Input:
N = 2
M[][] = {{0 1},
         {1 0}}
Output: -1
Explanation: The two people at the party both
know each other. None of them is a celebrity.


Your Task:
You don't need to read input or print anything. Complete the function celebrity() which takes the matrix M and its size N as input parameters and returns the index of the celebrity. If no such celebrity is present, return -1.


Expected Time Complexity: O(N)
Expected Auxiliary Space: O(1)


Constraints:
2 <= N <= 3000
0 <= M[][] <= 1

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The Celebrity Problem

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