Check whether an N \times N matrix is an Identity matrix (1s on the main diagonal, 0s everywhere else).

Difficulty: Hard

Phase: 6 · Mixed Logical Challenges

XP Reward: 30 XP

Topics: Mixed Logical Challenges, Hard

Supported Languages: Python, JavaScript, C, C++, Java

Problem Description

Given N followed by N x N matrix, check whether it is an Identity matrix (1s on main diagonal, 0s elsewhere). Print 'Yes' or 'No'. Input Format: Read input from standard input (stdin). Output Format: Print the result to standard output (stdout).

Constraints

-10^9 <= N <= 10^9

Examples

Example 1

Input: 3 1 0 0 0 1 0 0 0 1

Output: Yes

Explanation: Sample execution for input 3 1 0 0 0 1 0 0 0 1