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
#!/usr/bin/env python                                                                                          
#-*- coding: utf-8 -*-                                                                                         

from itertools import product

if __name__ == "__main__":
    N, M, K = map(int, raw_input().split())
    success = False
    for	n, m in	product(range(N+1), range(M+1)):
        if n*M + m*N - 2*n*m == K:
            success = True
            break
    if success:
        print "Yes"
    else:
        print "No"