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.Scanner;

public class Main {

	static Scanner scanner;

	public static void main(String[] args) {
	    scanner = new Scanner(System.in);

	    int N=gi();
	    int M=gi();
	    int K=gi();

	    for (int i=0; i<=N;i++) {
	    	for (int j=0; j<=M;j++) {
		    	int c=i*M+j*N-2*i*j;
		    	if(c==K) {
		    		System.out.println("Yes");
		    		return;
		    	}
		    }
	    }
	    

        System.out.println("No");
//	    if(max>s-max) {
//	    	System.out.println(s-max-1);
//	    }
	}

	// 文字列として入力を取得
	public static String gs() {
		return scanner.next();
	}

	// intとして入力を取得
	public static int gi() {
		return Integer.parseInt(scanner.next());
	}

	// longとして入力を取得
	public static long gl() {
		return Long.parseLong(scanner.next());
	}

	// doubleとして入力を取得
	public static double gd() {
		return Double.parseDouble(scanner.next());
	}
}