Problem Description

There is a grid of $ N $ rows and $ M $ columns, initially all squares are white.

Each row and each column has a button. Pressing a button in a row will invert the color of all squares in that row, i.e., white squares will turn black and black squares will turn white. Similarly, pressing a button in a column will invert the color of all squares in that column.

Takahashi can press the buttons any number of times. Determine if it is possible to have exactly $ K $ black squares.

Input Format

The input is given from the standard input in the following format:

$ N $ $ M $ $ K $

Output Format

If it is possible to have exactly $ K $ black squares, output Yes; otherwise, output No.

Sample Input and Output

Sample Input #1

2 2 2

Sample Output #1

Yes

Sample Input #2

2 2 1

Sample Output #2

No

Sample Input #3

3 5 8

Sample Output #3

Yes

Sample Input #4

7 9 20

Sample Output #4

No

Notes/Hints

Constraints

• $1 \leq N, M \leq 1000$
• $0 \leq K \leq$

Sample Explanation 1

Press the button in the first row, then the button in the first column.

Sample Explanation 3

Press the buttons in the first column, third column, second row, and fifth column in that order.

见题面 Input 部分

见题面 Output 部分