Problem:
Score : 200 points

Problem Statement

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.

Sample Input 1

10

Sample Output 1

9

There are four perfect powers that are at most 10: 1, 4, 8 and 9.
We should print the largest among them, 9.

Sample Input 2

1

Sample Output 2

1

Sample Input 3

999

Sample Output 3

961

Solution in PyPy3 (2.4.0) (judge verdict: Wrong Answer)

lis=[0]*1001
for i in range(2,int(1000**0.5)+1):
    point=2
    count=i
    while count<1000:
        try:
            count=i
            count=count**point
            lis[count]=1
            point +=1
        except:break
lis[1]=1
target=[]
for i in range(len(lis)):
    if lis[i]==1:
        target.append(i)

x=int(input())
ans=0
for i in target:
    if i<=x:
        ans=i
    elif x==1000:
        print(x)
        break
    else:print(ans);break