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
import java.io.*;
import java.math.*;
import java.util.*;
public class Main { //Simulate flip processes
	//UPD: Don't always need to take max rows
 
	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);
		int N = input.nextInt();
		int M = input.nextInt();
		int K = input.nextInt();
		System.out.println(Valid(N,M,K)?"Yes":"No");
	}	
	public static boolean Valid(int N,int M,int K) {
		for (int r = 0; r <= N; r++) {
			int numB = r*M;
			for (int c = 0; c <= M; c++) {
				int leftrows = N-r;
				int net = leftrows-r;
				int total = numB+c*net;
				if (total==K) {
					return true;
				}
			}
		}
		return false;
	}
}