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 C (Clang 3.8.0) (judge verdict: Accepted)

#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <inttypes.h>
#include <stdint.h>
#include <string.h>
#include <math.h>

static uint32_t getPowBLessThanOREqualToX(const uint32_t b, const uint32_t X) {
	uint32_t powB = b;
	while (1) {
		if (powB * b <= X) {
			powB *= b;
		}
		else {
			break;
		}
	}

	return powB;
}

int main(void) {
	uint32_t X;
	uint32_t maxPow = 1;

	scanf("%"PRIu32, &X);

	const uint32_t maxB = (uint32_t)sqrt((double)X);

	for (uint32_t b = 2; b <= maxB; b++) {
		const uint32_t maxPowBLessThanOrEqualToX = getPowBLessThanOREqualToX(b, X);
		if (maxPowBLessThanOrEqualToX > maxPow) {
			maxPow = maxPowBLessThanOrEqualToX;
		}
	}

	printf("%"PRIu32, maxPow);

	return 0;
}