N by N chessboard with N queens

Given an chessboard and N queens with their coordinates, you are asked if there are any two queens that attack each other.

Input

The first line of the input contains a single integer N (1 ≤ N ≤ 100).
The next N lines contain the coordinates of the queens (1 ≤ ≤ N).

Output

The program should print Yes in case there are queens attacking each other and No otherwise.

Examples

Input
Output
4 1 2 2 4 3 1 4 3
No
4 1 1 2 3 3 4 4 2
Yes

Explanation

notion image
Example 1
notion image
Example 2
 

Constraints

Time limit: 2 seconds

Memory limit: 512 MB

Output limit: 1 MB

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