You are in a party of N people, where only one person is known to everyone. Such a person may be present in the party, if yes, (s)he doesn’t know anyone in the party. Your task is to find the stranger (celebrity) in party.
You will be given a square matrix M[][] where if an element of row i and column j is set to 1 it means ith person knows jth person. You need to complete the function getId() which finds the id of the celebrity if present else return -1. The function getId() takes two arguments, the square matrix M and its size N.
Here, M[i][i] will be equal to zero.
Note: Expected time complexity is O(N) with constant extra space.
Input:
The first line of input contains an element T denoting the number of test cases. Then T test cases follow. Each test case consist of 2 lines. The first line of each test case contains a number denoting the size of the matrix M. Then in the next line are space separated values of the matrix M.
Output:
For each test case output will be the id of the celebrity if present (0 based index). Else -1 will be printed.
User Task:
The task is to complete the function getId() which returns the Id of celebrity if present, else -1.
Constraints:
1 <= T <= 50
2 <= N <= 501
0 <= M[][] <= 1
Example:
Input :
2
3
0 1 0 0 0 0 0 1 0
2
0 1 1 0
Output :
1
-1
Explanation :
Testcase 1:
For the above test case the matrix will look like
0 1 0
0 0 0
0 1 0
Here, the celebrity is the person with index 1 ie id 1
Testcase 2:
The matrix will look like
0 1
1 0
Here, there is no such person who is a celebrity (a celebrity should know no one).
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