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

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