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,i,j;
    cin>>n>>m>>k;
    bool flag=false;
    if(k==0)flag=true;
    for(i=0;i<=n;i++)
	  for(j=0;j<=m;j++){
    	  if(m*i+n*j-2*i*j==k)flag=true;
	  }
	if(flag)cout<<"Yes";else cout<<"No";
}