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 <bits/stdc++.h>
using namespace std;

int main() {
	
	int N, M, K;

	cin >> N >> M >> K;

	for (int n = 0; n <= N; ++n)
	for (int m = 0; m <= M; ++m)
	{
		if (n*M + m*N - 2*n*m == K)
		{
			cout << "Yes";
			return 0;
		}
	}

	cout << "No";

	return 0;
}