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<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int i,j,k,n,m,w;
int main(){
	scanf("%d%d%d",&n,&m,&w);
	for (i=0,k=0;!k&&i<=n;i++)
	 for (j=0;!k&&j<=m;j++)
	  if (m*i+n*j-2*i*j==w) k=1;
	puts(k?"Yes":"No");
	return 0;
}