We say that a 2-dimensional, rectangular word w of size n × m (imagine it as a board with letter written in the squares) can be tiled with a rectangular pattern p if there are such occurrences of p in w (but not necessarily all of them) that no two of them overlap and each symbol (square) of w is covered by one of them. Given such word w, find a rectangular pattern p of smallest size (area) which the word w can be tiled with.

Input

The first line of input contains a number t (1 ≤ t ≤ 100) that indicates the number of test cases to follow. Each test case begins with a line consisting of two positive integers n and m (1 ≤ n, m ≤ 1000) indicating dimensions of the board. n lines follow, each of them containing m small letters of the English alphabet (a, b ... z).

Output

For each test case output the smallest possible area of a pattern p that can be used to tile the given board.

Example

Input:
3
4 3
aaa
aaa
aaa
aaa
4 4
abab
cdcd
abab
cdcd
3 4
aaaa
aaaa
aaab

Output:
1
4
12