Penelope is playing a game on a grid! Her grid currently contains s, while the rest of her grid cells contain s.

Penelope isn't sure she likes her grid though. Specifically, she is worried that her grid isn't *beautiful*. A grid is beautiful if every row sum and column sum are even.

Penelope is in a hurry to make her grid beautiful so she asks you: how can she make her grid beautiful? On each move, you can flip the value of a grid cell: from to or to . Since she is in a hurry, she asks you to make her grid beautiful as fast as possible.

#### Constraints

All cells given are distinct.

##### Subtask 1 [30%]

##### Subtask 2 [70%]

No additional constraints.

#### Input Specification

The first line contains integers, , the number of rows; , the number of columns; and .

The next lines each contain two integers and , indicating that the cell in the row, column contains a .

#### Output Specification

On the first line output , the minimum number of moves required to make the grid beautiful. must satisfy . It can be proven that the minimum lies within this range.

On the next lines, output two space-separated integers and , indicating that you will flip the cell in the row, column.

You may output any valid sequence.

**Note: your output must follow the standard convention of not having any extra whitespace, and it must end with a new line.**

#### Scoring

If you output an incorrect value , but a valid sequence of moves, you will receive for that test case.

If you output a correct value , but an invalid sequence of moves, you will receive for that test case.

If you output a correct value of and any valid sequence of moves, you will receive for that test case.

Your score for a subtask will be the minimum score across all test cases of that subtask.

#### Sample Input

```
2 3 3
1 1
1 3
2 1
```

#### Sample Output

```
1
2 3
```

#### Explanation

Note that after our operation, our grid is:

```
1 0 1
1 0 1
```

which satisfies the constraints.

## Comments