CSES - KILO 2018 2/5 - Simplified Sudoku
  • Time limit: 1.00 s
  • Memory limit: 512 MB

You are given a grid of size n \times n whose each element is an integer between 1 and n.

Your task is to find out if every row and column contains n distinct values.

Input

The first line contains an integer n: the size of the grid.

After this, there are n lines which describe the grid. Each line has n integers between 1 and n.

Output

Print YES if every row and column contsina n distinct values and NO otherwise.

Constraints

  • 1 \le n \le 100

Example 1

Input:

3
1 2 3
2 3 1
3 1 2

Output:

YES

Example 2

Input:

3
1 1 1
1 1 1
1 1 1

Output:

NO