A grid-filling game has recently become popular worldwide: Given an $n \times m$ grid. The rows are numbered from $1$ to $n$ from top to bottom, and the columns are numbered from $1$ to $m$ from left to right. A cell is called an "odd cell" if both its row index and column index are odd. At the start of the game, all odd cells are filled with numbers. You need to fill in the remaining cells such that the grid satisfies the following conditions:

1. The sum of all numbers in any $a_1 \times b_1$ subgrid is greater than $0$.
2. The sum of all numbers in any $a_2 \times b_2$ subgrid is less than $0$.

Here, $a_1, b_1, a_2, b_2$ are given at the start of the game. An $a \times b$ subgrid is defined as the set of all cells with row indices between $i$ and $i+a-1$ (where $1 \le i \le n-a+1$) and column indices between $j$ and $j+b-1$ (where $1 \le j \le m-b+1$).

Little P likes this game very much and hopes you can help him write a program to provide a filling scheme, or tell him that no such scheme exists.

Input

The first line contains 6 positive integers $n, m, a_1, b_1, a_2, b_2$, all between $1$ and $100$.

Starting from the second line, there are $\lceil \frac{n+1}{2} \rceil$ lines, each containing $\lceil \frac{m+1}{2} \rceil$ integers. The $k$-th integer ($k=1, 2, \dots, \lceil \frac{m+1}{2} \rceil$) on the $(i+1)$-th line represents the integer filled in the cell at row $2i-1$ and column $2j-1$ at the start of the game.

These integers are between $-100$ and $100$.

Output

If no filling scheme exists, output a single line "No".

If a filling scheme exists, first output "Yes". Then, output $n$ lines, each containing $m$ space-separated integers, describing a filling scheme. Every integer in the output must be between $-10^9$ and $10^9$.

Examples

Input 1

3 3 2 2 3 3
1 1
1 1

Output 1

Yes
1 -1 1
-4 5 -4
1 -1 1

Note 1

After filling in the numbers, the sum of the numbers in any $2 \times 2$ subgrid is $1$; the sum of the numbers in any $3 \times 3$ subgrid is $-1$.