#P1422B. Nice Matrix

    ID: 1187 Type: RemoteJudge 1000ms 256MiB Tried: 0 Accepted: 0 Difficulty: (None) Uploaded By: Tags>greedyimplementationmath*1300

Nice Matrix

No submission language available for this problem.

Description

A matrix of size n×mn \times m is called nice, if all rows and columns of the matrix are palindromes. A sequence of integers (a1,a2,,ak)(a_1, a_2, \dots , a_k) is a palindrome, if for any integer ii (1ik1 \le i \le k) the equality ai=aki+1a_i = a_{k - i + 1} holds.

Sasha owns a matrix aa of size n×mn \times m. In one operation he can increase or decrease any number in the matrix by one. Sasha wants to make the matrix nice. He is interested what is the minimum number of operations he needs.

Help him!

The first line contains a single integer tt — the number of test cases (1t101 \le t \le 10). The tt tests follow.

The first line of each test contains two integers nn and mm (1n,m1001 \le n, m \le 100) — the size of the matrix.

Each of the next nn lines contains mm integers ai,ja_{i, j} (0ai,j1090 \le a_{i, j} \le 10^9) — the elements of the matrix.

For each test output the smallest number of operations required to make the matrix nice.

Input

The first line contains a single integer tt — the number of test cases (1t101 \le t \le 10). The tt tests follow.

The first line of each test contains two integers nn and mm (1n,m1001 \le n, m \le 100) — the size of the matrix.

Each of the next nn lines contains mm integers ai,ja_{i, j} (0ai,j1090 \le a_{i, j} \le 10^9) — the elements of the matrix.

Output

For each test output the smallest number of operations required to make the matrix nice.

Samples

Sample Input 1

2
4 2
4 2
2 4
4 2
2 4
3 4
1 2 3 4
5 6 7 8
9 10 11 18

Sample Output 1

8
42

Note

In the first test case we can, for example, obtain the following nice matrix in 88 operations:


2 2
4 4
4 4
2 2

In the second test case we can, for example, obtain the following nice matrix in 4242 operations:


5 6 6 5
6 6 6 6
5 6 6 5