Idempotent Matrix Verification

Determine if a given N * N matrix is an idempotent matrix. A matrix is considered idempotent if it satisfies the following condition:

M * M = M

Input:

The first line contains a single integer N, denoting the size of the matrix. The next N lines each contain N space-separated integers, representing the elements of the matrix.

Output:

Output 'true' if the matrix is idempotent; otherwise, output 'false'.

Example:

Input:

2
1 0
0 1

Output:

true

Constraints:

• 1 <= N <= 10³

Note

This task only requires determining the property of the matrix without additional output formatting.