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;
	bool a = false;
	for (int i = 0; i <= n && !a; i++) {
		for (int j = 0; j <= m && !a; j++) {
			a = i * (m - j) + (n - i) * j == k;
		}
	}
	cout << (a ? "Yes" : "No") << endl;
	return 0;
}
