We have a grid with N rows and M columns of squares. Initially, all the squares are white.

There is a button attached to each row and each column. When a button attached to a row is pressed, the colors of all the squares in that row are inverted; that is, white squares become black and vice versa. When a button attached to a column is pressed, the colors of all the squares in that column are inverted.

Takahashi can freely press the buttons any number of times. Determine whether he can have exactly K black squares in the grid.

Constraints

* 1 \leq N,M \leq 1000
* 0 \leq K \leq NM

Input

Input is given from Standard Input in the following format:


N M K


Output

If Takahashi can have exactly K black squares in the grid, print `Yes`; otherwise, print `No`.

Examples

Input

2 2 2


Output

Yes


Input

2 2 1


Output

No


Input

3 5 8


Output

Yes


Input

7 9 20


Output

No
#include<iostream>
#include<cstdio>

int N,M,K;

int main()
{
	int i,j;
	scanf("%d%d%d",&N,&M,&K);
	bool ans=false;
	for(i=1;i<=N;i++)
		for(j=1;j<=M;j++)
			if(i*j+(N-i)*(M-j)==K)
				ans=true;
	if(!K)ans=true;
	if(ans) puts("Yes");
	else puts("No");
	return 0;
}
