Problem Statement

You are given a matrix $A$ whose elements are non-negative integers. For a pair of integers $(i, j)$ such that $1 \\leq i \\leq H$ and $1 \\leq j \\leq W$, let $A_{i, j}$ denote the element at the $i$-th row and $j$-th column of $A$.

Let us perform the following procedure on $A$.

• First, replace each element of $A$ that is $0$ with an arbitrary positive integer (if multiple elements are $0$, they may be replaced with different positive integers).

• Then, repeat performing one of the two operations below, which may be chosen each time, as many times as desired (possibly zero).

  • Choose a pair of integers $(i, j)$ such that $1 \\leq i \\lt j \\leq H$ and swap the $i$-th and $j$-th rows of $A$.
  • Choose a pair of integers $(i, j)$ such that $1 \\leq i \\lt j \\leq W$ and swap the $i$-th and $j$-th columns of $A$.

Determine whether $A$ can be made to satisfy the following condition.

• $A_{1, 1} \\leq A_{1, 2} \\leq \\cdots \\leq A_{1, W} \\leq A_{2, 1} \\leq A_{2, 2} \\leq \\cdots \\leq A_{2, W} \\leq A_{3, 1} \\leq \\cdots \\leq A_{H, 1} \\leq A_{H, 2} \\leq \\cdots \\leq A_{H, W}$.

• In other words, for every two pairs of integers $(i, j)$ and $(i', j')$ such that $1 \\leq i, i' \\leq H$ and $1 \\leq j, j' \\leq W$, both of the following conditions are satisfied.

  • If $i \\lt i'$, then $A_{i, j} \\leq A_{i', j'}$.
  • If $i = i'$ and $j \\lt j'$, then $A_{i, j} \\leq A_{i', j'}$.

Constraints

• $2 \\leq H, W$
• $H \\times W \\leq 10^6$
• $0 \\leq A_{i, j} \\leq H \\times W$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

$H$ $W$ $A_{1, 1}$ $A_{1, 2}$ $\\ldots$ $A_{1, W}$ $A_{2, 1}$ $A_{2, 2}$ $\\ldots$ $A_{2, W}$ $\\vdots$ $A_{H, 1}$ $A_{H, 2}$ $\\ldots$ $A_{H, W}$

Output

If $A$ can be made to satisfy the condition in the problem statement, print Yes; otherwise, print No.

Sample Input 1

3 3
9 6 0
0 4 0
3 0 3

Sample Output 1

Yes

One can perform the operations as follows to make $A$ satisfy the condition in the problem statement, so you should print Yes.

• First, replace the elements of $A$ that are $0$, as shown below:

9 6 8
5 4 4
3 1 3

• Swap the second and third columns. Then, $A$ becomes:

9 8 6
5 4 4
3 3 1

• Swap the first and third rows. Then, $A$ becomes:

3 3 1
5 4 4
9 8 6

• Swap the first and third columns. Then, $A$ becomes the following and satisfies the condition in the problem statement.

1 3 3
4 4 5
6 8 9

Sample Input 2

2 2
2 1
1 2

Sample Output 2

No

There is no way to perform the operations to make $A$ satisfy the condition in the problem statement, so you should print No.