Matrix Reduction

Alex and Andrei are playing a game on an $N \cdot M$ matrix filled with non-negative integers. The rows of the matrix are numbered from $1$ to $N$ (from top to bottom), and the columns are numbered from $1$ to $M$ (from left to right).

Alex is allowed to perform the following operation any number of times:

• Choose a horizontal or vertical $1 \cdot 3$ subrectangle.
• Select an integer $V$.
• Add $V$ to all numbers in the chosen subrectangle, ensuring that no number becomes negative.

Andrei believes that Alex cannot make all the numbers in the matrix zero within at most $2 \cdot N \cdot M$ operations.

Alex is determined to prove him wrong -- but since he hasn't learned addition at school yet, he needs your help. Can you determine whether Alex can reduce the entire matrix to zero within the given limit?

Input data

The first line of the input contains two integers: $N$ and $M$.

Each of the next $N$ lines contains $M$ non-negative integers, representing the elements of the matrix.

Output data

First, print YES if it is possible to make all $A_{i,j}$ equal to zero within at most $2 \cdot N \cdot M$ operations. Otherwise, print NO.

If the answer is YES, proceed with the following output:

• Print an integer $R$, the number of operations perfomed.
• Print $R$ lines, each describing an operation in the format: $X_1 \ Y_1 \ X_2 \ Y_2 \ V$ where $(X_1, Y_1)$ are the coordinates of the top-left corner of the chosen subrectangle, $(X_2, Y_2)$ are the coordinates of the bottom-right corner of the subrectangle (that is, $X_1 \le X_2$ and $Y_1 \le Y_2$), and $V$ is the integer added to all elements within the subrectangle.

If there are multiple valid solutions, you can print any of them.

Constraints and clarifications

• $3 \le N \le 500$.
• $3 \le M \le 500$.
• $0 \le A_{i,j} \le 1 \ 000$ for each $i=1\ldots N$ and $j=1\ldots M$.
• $-10^9 \le V \le 10^9$.

Example 1

stdin

3 3
1 5 1
2 6 2
8 12 8

stdout

YES
6
1 1 1 3 8
2 1 2 3 7
3 1 3 3 1
1 1 3 1 -9
1 2 3 2 -13
1 3 3 3 -9

Explanation

In the first sample case, there are multiple valid solutions, with the sample output being one of them.

Example 2

stdin

3 3
1 5 0
2 6 2
8 12 8

stdout

NO

Explanation

In the second sample case it can be proven that no sequence of at most $2 \cdot N \cdot M = 18$ operations will lead to a matrix containing only zeros.