Problem B. Texture Tile ≡

Author:A. Klenin, T. Chistyakov   Time limit:2 sec
Input file:input.txt   Memory limit:256 Mb
Output file:output.txt  

Statement

Square raster image is represented by an array of N × N pixels. A texture tile is a square image in which the first row is equal to the last one, and the first column is equal to the last one. This property is valuable when covering the surface of graphics object with repeating copies of texture, because it allows "seamless" transitions between tiles.

Your program must, given an image, find its largest subimage which is a texture tile.

Input file format

Input file contains integer N followed by N2 numbers ci, j — pixel values.

Output file format

Output file must contain numbers p q m — coordinates of top left corner and size of the largest texture tile. If several solutions exist, output any of them.

Constraints

1 ≤ N ≤ 370, 0 ≤ ci, j ≤ 255.

Sample tests

No. Input file (input.txt) Output file (output.txt)
1 
2
0 0
2 3
 
1 1 1
2 
4
1 0 0 0
1 2 5 2
1 0 0 0
4 4 4 4
 
1 2 3
0.070s 0.010s 13