Bobo has written an $n \times m$ matrix $A_{i, j}$.

• Initially, he sets all elements $A_{i, j}$ ($1 \leq i \leq n, 1 \leq j \leq m$) to 0.
• Then, he chooses $4$ integers $x_1, x_2, y_1, y_2$ such that $1 \leq x_1 \leq x_2 \leq n$ and $1 \leq y_1 \leq y_2 \leq m$, and sets all elements $A_{i, j}$ satisfying $x_1 \leq i \leq x_2$ and $y_1 \leq j \leq y_2$ to 1.

Given an $n \times m$ matrix $A_{i, j}$, determine whether it is a matrix that could have been written by Bobo.

Input

The input contains multiple test cases. Process until the end of the file.

Each test case starts with two integers $n$ and $m$.

The next $n$ lines each contain $m$ integers $A_{i, 1}, A_{i, 2}, \dots, A_{i, m}$.

• $1 \leq n, m \leq 10$
• $A_{i, j} \in \{0, 1\}$
• At most $1000$ test cases.

Output

For each test case, output Yes if the given matrix could have been written by Bobo, otherwise output No.

Examples

Input 1

2 2
11
10
3 3
000
001
000
3 4
1111
1111
1111

Output 1

No
Yes
Yes