Madoka and the Elegant Gift

题意翻译

在一个 $01$ 矩阵中，称一个子矩形为黑色的，当且仅当其包含的都为黑色($1$)。称一个黑色子矩形为好的，当且仅当其不是另一个黑色子矩形的子矩形。称这个 $01$ 矩阵为优雅的，当且仅当不存在两个有公共格子的好的子矩形。 你的任务是，判断一个矩阵是否为优雅的。

题目描述

Madoka's father just reached $ 1 $ million subscribers on Mathub! So the website decided to send him a personalized award — The Mathhub's Bit Button! The Bit Button is a rectangular table with $ n $ rows and $ m $ columns with $ 0 $ or $ 1 $ in each cell. After exploring the table Madoka found out that: - A subrectangle $ A $ is contained in a subrectangle $ B $ if there's no cell contained in $ A $ but not contained in $ B $ . - Two subrectangles intersect if there is a cell contained in both of them. - A subrectangle is called black if there's no cell with value $ 0 $ inside it. - A subrectangle is called nice if it's black and it's not contained in another black subrectangle. - The table is called elegant if there are no two nice intersecting subrectangles. For example, in the first illustration the red subrectangle is nice, but in the second one it's not, because it's contained in the purple subrectangle. Help Madoka to determine whether the table is elegant.

输入输出格式

输入格式

Each test contains multiple test cases. The first line contains a single integer $ t $ ( $ 1 \le t \le 200 $ ) — the number of test cases. Description of the test cases follows. The first line of each test case contains two positive integers $ n, m $ ( $ 1 \le n, m \le 100 $ ). The next $ n $ lines contain strings of length $ m $ consisting of zeros and ones — the description of the table. It is guaranteed that the sum of the values of $ n $ and the sum of the values of $ m $ for all test cases do not exceed $ 777 $ .

输出格式

For each test case print "YES" if its table is elegant or print "NO" otherwise. You may print each letter in any case (for example, "YES", "Yes", "yes", "yEs" will all be recognized as positive answer).

输入输出样例

输入样例 #1

5
3 3
100
011
011
3 3
110
111
110
1 5
01111
4 5
11111
01010
01000
01000
3 2
11
00
11

输出样例 #1

YES
NO
YES
NO
YES

说明

In the second test case the table is not elegant, because the red and the purple subrectangles are nice and intersect. In the fourth test case the table is not elegant, because the red and the purple subrectangles are nice and intersect. 

题意翻译

在一个 $01$ 矩阵中，称一个子矩形为黑色的，当且仅当其包含的都为黑色($1$)。称一个黑色子矩形为好的，当且仅当其不是另一个黑色子矩形的子矩形。称这个 $01$ 矩阵为优雅的，当且仅当不存在两个有公共格子的好的子矩形。 你的任务是，判断一个矩阵是否为优雅的。