Problems

Cut Board

A rectangular board of size n * m has 1 * 1 cells. x consecutive cells from the first row starting from the top-left and y consecutive cells from the last row starting from the bottom-right are cut off. Can you fill all the cells of the remaining board using some 2 * 1 dominoes such that none overlap or hang off the edge?

Write the program which takes in four integers n, m, x and y and prints whether the remaining board can be filled with dominoes, and if yes, prints one way to place the dominoes.

Input

Consists of a single line containing four space-separated integers n, m, x and y (3n, m100, 1x, y < m).

Output

Print NO in a single line if you cannot fill all the cells of the cut board using dominoes.

Otherwise, print YES in the first line, and a single integer in the second line denoting the number of dominoes required.

In the next lines, print four space-separated integers denoting the location of the domino. The x-coordinate corresponds to the row number and the y-coordinate corresponds to the column number.

If the location of domino is `x1`, `y1`, `x2`, `y2` then it is present at cells (`x1`, `y1`) and (`x2`, `y2`).

You can fill the board by placing each domino either vertically or horizontally.

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

Time limit 1 second
Memory limit 128 MiB
Input example #1
```3 4 1 3
```
Output example #1
```YES
4
2 1 3 1
2 2 2 3
1 2 1 3
1 4 2 4
```
Input example #2
```3 3 2 2
```
Output example #2
```NO
```