For an $n \times m$ matrix $A_{i, j}$, Bobo defines the distance between row $i$ and row $j$ as $d(i, j) = \sum_{k = 1}^m |A_{i, k} - A_{j, k}|$, where $|x|$ denotes the absolute value of $x$. Bobo calls the matrix $A_{i, j}$ an odd matrix if $d(i, j)$ is odd for all $1 \leq i < j \leq n$.

Given a matrix $A_{i, j}$, determine whether it is an odd matrix.

Input

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

Each test case starts with a line containing two integers $n$ and $m$. The next $n$ lines each contain $m$ integers $A_{i, 1}, \dots, A_{i, m}$.

• $1 \leq n, m \leq 10^3$
• $0 \leq A_{i, j} < 10$
• The sum of $n \times m$ does not exceed $2 \times 10^6$.

Output

For each test case, output Yes if it is an odd matrix, otherwise output No.

Examples

Input 1

1 2
0 0
2 3
1 2 3
2 1 4
3 3
1 2 3
4 5 6
7 8 9

Output 1

Yes
Yes
No