K. glimmerypond
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Daniel is given a 2D grid representing an $$$n \times m$$$ pond, where each cell can either be filled with water or be empty. The grid is considered glimmery if the number of water-filled cells in any square subgrid of size $$$k \times k$$$ is divisible by 2.

Help Daniel write a function that determines whether a given pond is glimmery or not.

Input

The input parameters are:

$$$n, m, k$$$ each separated by a single space. $$$n$$$ is the number of rows in the pond. $$$m$$$ is the number of columns in the pond. Both $$$n, m$$$ satisfy $$$1\le n, m\le 100$$$. $$$k$$$ satisfies $$$1\le k\le \min(n, m)$$$.

This is followed by $$$n$$$ lines. Each line contains $$$m$$$ integers, where 0 denotes an empty cell and 1 represents a water-filled cell.

Output

Ouput "true" if the pond is glimmery, "false" if not.

Example
Input
4 3 2
1 1 0
1 0 0
0 1 0
1 1 1
Output
true