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<iostream>

using namespace std;

int n,m,k,i,j;

int main()
{
    cin>>n>>m>>k;
	for(int i=0;i<=n;i++)
	    for(int j=0;j<=m;j++)
		    if((n-i)*j+(m-j)*i==k){puts("Yes");return 0;}
	puts("No");
}