Painting

We have a grid with H rows and W columns, where all the squares are initially white.

You will perform some number of painting operations on the grid. In one operation, you can do one of the following two actions:

• Choose one row, then paint all the squares in that row black.
• Choose one column, then paint all the squares in that column black.

At least how many operations do you need in order to have N or more black squares in the grid? It is guaranteed that, under the conditions in Constraints, having N or more black squares is always possible by performing some number of operations.

Constraints

• 1 \leq H \leq 100
• 1 \leq W \leq 100
• 1 \leq N \leq H \times W
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

H W N

Output

Print the minimum number of operations needed.

Examples

Input

3 7 10

Output

2

Input

14 12 112

Output

8

Input

2 100 200

Output

2

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

H W N

outputFormat

Output

Print the minimum number of operations needed.

Examples

Input

3 7 10

Output

2

Input

14 12 112

Output

8

Input

2 100 200

Output

2

样例

3
7
10

2