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 JAVA):

Solution:
import java.util.Scanner;

public class E1
{
    public static void main(String[] args)
    {
        Scanner s = new Scanner(System.in);
        int q = s.nextInt();
        for (int qi = 0; qi < q; qi++)
        {
            int h = s.nextInt();
            int w = s.nextInt();

            int[][] rows4 = new int[4][w];
            for (int i = 0; i < w; i++)
            {
                rows4[0][i] = s.nextInt();
            }
            for (int i = 0; i < h / 2 - 1; i++)
            {
                s.nextLine();
            }
            for (int i = 0; i < w; i++)
            {
                rows4[1][i] = s.nextInt();
            }
            for (int i = 0; i < w; i++)
            {
                rows4[2][i] = s.nextInt();
            }
            for (int i = 0; i < h / 2 - 1; i++)
            {
                s.nextLine();
            }
            for (int i = 0; i < w; i++)
            {
                rows4[3][i] = s.nextInt();
            }

            int s1 = diff(rows4[0], rows4[3]);
            int s2 = diff(rows4[1], rows4[2]);
            boolean rearr = s1 < s2;
            System.out.println(rearr ? "YES" : "NO");
        }
    }

    static int diff(int[] r1, int[] r2)
    {
        int score = 0;
        for (int i = 1; i < r1.length; i++)
        {
            score += sq(r1[i] - r2[i]) +
                    sq(r1[i] - r2[i - 1]) +
                    sq(r1[i - 1] - r2[i]);
        }
        return score;
    }

    static int sq(int i)
    {
        return i * i;
    }
}