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.util.*;
import java.io.*;

public class Main{

	public static void main(String[] args){
		solve();
	}

	public static void solve(){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		int k = sc.nextInt();
		boolean flag = false;
		for(int i=0;i<=n;i++){
			for(int j=0;j<=m;j++){
				if(i*m + j*n - 2*i*j == k){
					flag = true;
					break;
				}
			}
			if(flag){
				break;
			}
		}
		if(flag){
			System.out.println("Yes");
		}
		else{
			System.out.println("No");
		}
	}
}

