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N by N chessboard with N queens

Given an chessboard and 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 .
The next lines contain the coordinates of the queens .

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

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Example 1
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Example 2
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