Quad Tree Compression

You are given an N x N black-and-white image made only of 0 and 1. If every cell in a region has the same value, that region is represented by that one character. If a region contains both values, divide it into four equal parts and compress them in this order: upper left, upper right, lower left, lower right. Wrap the four compressed results in parentheses.

Print the compressed string for the entire image.

The first line contains the image size N. N is a power of 2, and 1 <= N <= 64. The next N lines each contain a string of length N. Each character is either 0 or 1 and represents one cell of the image.

Print the compressed string for the entire image.