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Chessboard

Problem Description
A chessboard is a NxN binary matrix with rows and columns numbered from 1 to N. Each position of the matrix is black (1) if the sum of the row number and the column number is even; otherwise it is white (0). The following pictures show how a chessboard looks like for N=1, 2 and 3.

Given a NxN binary matrix, find the size of the largest chessboard completely located inside the matrix, as well as the number of chessboards having the largest size (these chessboards may overlap).

Input
The first line of input contains an integer number T, representing the number of test cases to follow. Each test case contains on the first line an integer number N (1<=N<=2000), representing the number of rows and columns of the given matrix. The next N lines describe the matrix: each line contains N characters, which may be either ‘1’ (denoting a black square) or ‘0’ (denoting a white square); at the end of each line there will be a new line character. The matrix will contain at least one ‘1’ character.

Output
For each of the T test cases, in the order given in the input, print one line containing the number of rows and colums of the largest chessboard, followed by a blank and then the number of chessboards having the largest size.

Sample Input
1
5
00101
11010
00101
01010
11101

Sample Output
3 3

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