B. Pushing Ballstime limit per test1 secondmemory limit per test512 megabytesinputstandard inputoutputstandard outputEcrade has an $$$n \times m$$$ grid, originally empty, and he has pushed several (possibly, zero) balls in it.Each time, he can push one ball into the grid either from the leftmost edge of a particular row or the topmost edge of a particular column of the grid.When a ball moves towards a position: If there is no ball originally at that position, the incoming ball will stop and occupy the position. If there is already a ball at that position, the incoming ball will stop and occupy the position, while the original ball will continue moving to the next position in the same direction. Note that if a row or column is full (i.e., all positions in that row or column have balls), he cannot push a ball into that row or column.Given the final state of whether there is a ball at each position of the grid, you need to determine whether it is possible for Ecrade to push the balls to reach the final state.InputThe first line contains an integer $$$t$$$ ($$$1 \le t \le 10\,000$$$) — the number of test cases. The description of the test cases follows.The first line of each test case contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n, m \le 50$$$).This is followed by $$$n$$$ lines, each containing exactly $$$m$$$ characters and consisting only of $$$0$$$ and $$$1$$$, describing the final state of the grid. There is a ball at one position of the grid if and only if the corresponding position of the given input is $$$1$$$.It is guaranteed that the sum of $$$n\cdot m$$$ over all test cases does not exceed $$$10\,000$$$.OutputFor each test case, output "Yes" (without quotes) if it is possible for Ecrade to push the balls to reach the final state, and "No" (without quotes) otherwise.You can output "Yes" and "No" in any case (for example, strings "YES", "yEs" and "yes" will be recognized as a positive response).ExampleInput53 30010011103 30101110103 31111111113 30000000003 3000000001OutputYES
YES
YES
YES
NO
NoteFor simplicity, if Ecrade pushes a ball from the leftmost edge of the $$$i$$$-th row, we call the operation $$$\text{ROW}\ i$$$; if he pushes a ball from the topmost edge of the $$$i$$$-th column, we call the operation $$$\text{COL}\ i$$$.For intuitive understanding, a non-zero number $$$x$$$ in the matrix given below represents the $$$x$$$-th ball that is pushed in.In the first test case, a possible series of operations:$$$\begin{pmatrix}0&0&0\\0&0&0\\0&0&0\end{pmatrix}\xrightarrow{\text{ROW}\ 3}\xrightarrow{\text{ROW}\ 3} \begin{pmatrix}0&0&0\\0&0&0\\2&1&0\end{pmatrix}\xrightarrow{\text{COL}\ 3}\xrightarrow{\text{COL}\ 3} \begin{pmatrix}0&0&4\\0&0&3\\2&1&0\end{pmatrix}$$$In the second test case, a possible series of operations:$$$\begin{pmatrix}0&0&0\\0&0&0\\0&0&0\end{pmatrix}\xrightarrow{\text{ROW}\ 2}\xrightarrow{\text{ROW}\ 2}\xrightarrow{\text{ROW}\ 2} \begin{pmatrix}0&0&0\\3&2&1\\0&0&0\end{pmatrix}\xrightarrow{\text{COL}\ 2}\xrightarrow{\text{COL}\ 2} \begin{pmatrix}0&5&0\\3&4&1\\0&2&0\end{pmatrix}$$$In the third test case, a possible series of operations:$$$\begin{pmatrix}0&0&0\\0&0&0\\0&0&0\end{pmatrix}\xrightarrow{\text{ROW}\ 1}\xrightarrow{\text{ROW}\ 2}\xrightarrow{\text{ROW}\ 3} \begin{pmatrix}1&0&0\\2&0&0\\3&0&0\end{pmatrix}\xrightarrow{\text{COL}\ 3}\xrightarrow{\text{COL}\ 3}\xrightarrow{\text{COL}\ 3} \begin{pmatrix}1&0&6\\2&0&5\\3&0&4\end{pmatrix}\xrightarrow{\text{ROW}\ 1}\xrightarrow{\text{ROW}\ 2}\xrightarrow{\text{ROW}\ 3} \begin{pmatrix}7&1&6\\8&2&5\\9&3&4\end{pmatrix}$$$