Exponential

You are given a positive integer X. Find the largest perfect power that is at most X. Here, a perfect power is an integer that can be represented as b^p, where b is an integer not less than 1 and p is an integer not less than 2.

Constraints

• 1 ≤ X ≤ 1000
• X is an integer.

Input

Input is given from Standard Input in the following format:

X

Output

Print the largest perfect power that is at most X.

Examples

Input

10

Output

9

Input

1

Output

1

Input

999

Output

961

inputFormat

Input

Input is given from Standard Input in the following format:

X

outputFormat

Output

Print the largest perfect power that is at most X.

Examples

Input

10

Output

9

Input

1

Output

1

Input

999

Output

961

样例

10

9