Glue!

Interview

Time limit2sMemory limit1024 MB

Summary

Given a grid of piece labels, check that every label covers exactly k cells and that each piece is connected through shared sides.

Level: Medium4 of 10
Topics: BFS, Hash map, Matrix
Solved: No attempts yet

Problem

In the basic-level problem "Cut!" of a previous online olympiad, contestants had to cut a sheet of graph paper. The sheet could only be cut along the grid lines, and each resulting piece had to consist of exactly $k$ cells of the original sheet.

In this problem, you solve the jury's task: determine whether the team cut the sheet correctly.

Input

The first line contains two integers $n$ and $m$ ( $1 \le n, m \le 100$ ), the height and width of the sheet in cells. The second line contains $k$ ( $1 \le k \le 1000$ ). It is guaranteed that $n \cdot m$ is divisible by $k$ .

Each of the next $n$ lines contains $m$ integers. Each integer is the number of the piece that the team assigned to that cell. Pieces are numbered with positive integers starting from 1.

Output

If the team cut the sheet correctly, print OK. Otherwise, print Wrong answer.

Examples3

Example 1
Input
```
4 3
6
1 1 2
1 2 2
1 2 2
1 1 2
```
Expected output
```
OK
```
Example 2
Input
```
2 2
1
1 1
2 3
```
Expected output
```
Wrong answer
```
Example 3
Input
```
2 2
2
1 2
2 1
```
Expected output
```
Wrong answer
```