Problem: The Human-Cow Confederation (HC2), led by Heidi, has built a base where people and cows can hide, guarded from zombie attacks. The entrance to the base is protected by an automated gate which performs a kind of a Turing test: it shows the entering creature a photograph and asks them whether the top and bottom halves of this photograph have been swapped or not. A person (or even a cow) will have no problem answering such questions; on the other hand, a zombie would just randomly smash one of the two buttons.

The creature is asked a series of such questions. If at least 75% of them are answered correctly, the gate is unlocked; otherwise, a side door opens, beneath which a huge fan is spinning...

Heidi is now building a robot army to fight the zombies, and she wants the robots to also be able to enter the base. You are tasked with programming them to distinguish the images.

<image>

The first two images from the test set. The first picture has been rearranged, but not the second.

Input

The first line of the input contains the number q of questions (1 ≤ q ≤ 220). After that, q questions follow, each of which in the format described below.

The first line of every question contains two space-separated integers h and w (1 ≤ h, w ≤ 600) – the height (number of rows) and width (number of columns) of the photograph. (Most photographs are roughly 200 × 300.) After this, h lines follow, each describing a single row of the picture. The picture is monochrome (in shades of grey). Its i-th row is described by w space-separated integers aij (j = 1, ..., w), where aij is the brightness of the corresponding pixel (0 ≤ aij < 256, where 0 is black and 255 is white).

Each picture will be either a real-life photograph, or a real-life photograph which has been broken up into two pieces and rearranged. More precisely, in the latter case, the topmost <image> rows have been moved to the bottom of the picture. It is guaranteed that h is even.

There is only a single input file to be processed, called all.in, and it is downloadable from the online judge. You are also a given another input file, called sample.in, which contains the first 20 pictures from all.in; you are provided the correct answers for sample.in in sample.out. You are also given a directory easy_bmp, which contains the first 50 input photographs in the form of .bmp image files, as well as a directory easy_sample_original_bmp, which contains the first 20 images before rearrangement. Check the notes for the download links.

Output

Your program should print q lines. The i-th line should contain your answer for the i-th question: YES if the photograph has been rearranged and NO otherwise. Your answers will be accepted if they all conform to this format and if at least 75% of them are correct.

Because the input is rather huge, feel free to process it locally and submit just your precomputed answers (i.e., a program which just prints your output for the input file all.in).

Note

The link to download all necessary files is http://assets.codeforces.com/files/690/easy_contestant_package.zip

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <typename T>
inline void read(T& a) {
  a = 0;
  char c;
  bool f = 0;
  while (!isdigit(c = getchar()))
    if (c == '-') f = 1;
  do a = a * 10 + c - '0';
  while (isdigit(c = getchar()));
  if (f) a = -a;
}
const int INF = 0x7fffffff;
const long double eps = 1e-8;
const long long MOD = 1e9 + 7;
const int MAXN = 800;
const int MAXM = 800;
int A[MAXN][MAXM];
void solve(int x) {
  int H, W;
  read(H);
  read(W);
  for (int i = 1; i <= H; ++i)
    for (int j = 1; j <= W; ++j) read(A[i][j]);
  int H0 = H / 2;
  double e = 0;
  for (int i = 1; i <= W - 3; ++i) {
    int p = A[H0][i] + A[H0][i + 1] + A[H0][i + 2];
    int q = A[H0 + 1][i] + A[H0 + 1][i + 1] + A[H0 + 1][i + 2];
    int w = (p + q) / 2;
    double t = abs((double)(p - w) / (255 * 3));
    e += t / (W - 2);
  }
  puts(e < 0.04 ? "NO" : "YES");
}
int main(int argc, char* argv[]) {
  int Q;
  read(Q);
  for (int i = 1; i <= Q; ++i) solve(i);
  return 0;
}