Contest Duration: ~ (local time)
B - fLIP

Time Limit: 2 sec / Memory Limit: 256 MB

### 問題文

NM 列のマス目があり、最初は全てのマスが白いです。

### 制約

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

### 入力

N M K


### 入力例 1

2 2 2


### 出力例 1

Yes


1 行目、 1 列目の順にボタンを押せばよいです。

### 入力例 2

2 2 1


### 出力例 2

No


### 入力例 3

3 5 8


### 出力例 3

Yes


1 列目、3 列目、2 行目、5 列目の順にボタンを押せばよいです。

### 入力例 4

7 9 20


### 出力例 4

No


Score : 200 points

### Problem Statement

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.

### Sample Input 1

2 2 2


### Sample Output 1

Yes


Press the buttons in the order of the first row, the first column.

### Sample Input 2

2 2 1


### Sample Output 2

No


### Sample Input 3

3 5 8


### Sample Output 3

Yes


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

### Sample Input 4

7 9 20


### Sample Output 4

No