Beautiful Garden

Time Limit: 1000 ms Memory Limit: 65536 KiB

Problem Description

There\'s a beautiful garden whose size is n × m in Edward\'s house. The garden can be
partitioned into n × m equal-sized square chunks. There are some kinds of flowers
planted in each square chunk which can be represented by using lowercase letters.
However, Edward thinks the garden is not beautiful enough. Edward wants to build a
water pool in the garden. So that the garden would look like symmetric (both
horizontally and vertically). The water pool is a rectangle whose size is p × q and the
center of the water pool is also the center of the garden.
Something else important you should know is:
 n, m, p and q are all even.
 p is always less than n.
 q is always less than m.
 The borders of the water pool are parallel to the border of garden.
Edward wants to know how many different pairs of (p, q) he can choose.

Input

 There are multiple test cases. The first line of input contains an integer T indicating
the number of test cases. For each test case:
The first line contains two integers n and m (1 <= n, m <= 2000, n and m are even),
indicating the size of the garden. For next n lines, each line contains m characters
showing the garden.
It is guaranteed that only lowercase letters will appear.

Output

 For each test case, output an integer indicating the number of choices to build the
water pool.

Sample Input

3
6 8
acbbbbca
dcaccacd
cdaddadc
cdaddadc
dcaccacd
acbbbbca
6 8
acbcbbca
dcaccacd
cdaddadc
cdaddadc
dcaccacd
acbbbbca
6 8
acbbbbca
dcadcacd
cdaddadc
cdaddadc
dcaccacd
acbbbbca

Sample Output

6
0
3

Hint

 

Source

Ningbo_2014_Contest