Problem:
Score : 300 points

Problem Statement

Given is a positive integer L.
Find the maximum possible volume of a rectangular cuboid whose sum of the dimensions (not necessarily integers) is L.

Constraints

1 ≤ L ≤ 1000

L is an integer.

Input

Input is given from Standard Input in the following format:

L

Output

Print the maximum possible volume of a rectangular cuboid whose sum of the dimensions (not necessarily integers) is L.
Your output is considered correct if its absolute or relative error from our answer is at most 10^{-6}.

Sample Input 1

3

Sample Output 1

1.000000000000

For example, a rectangular cuboid whose dimensions are 0.8, 1, and 1.2 has a volume of 0.96.

On the other hand, if the dimensions are 1, 1, and 1, the volume of the rectangular cuboid is 1, which is greater.

Sample Input 2

999

Sample Output 2

36926037.000000000000

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <algorithm>
#include <cassert>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <vector>

using namespace std;

typedef long long ll;

template<class T>
inline bool chmax(T &a, T b) {
    if(a < b) {
        a = b;
        return true;
    }
    return false;
}

template<class T>
inline bool chmin(T &a, T b) {
    if(a > b) {
        a = b;
        return true;
    }
    return false;
}

int main(void) {
    double L;
    cin >> L;

    double ans = 0;
    for (double a = 0.01; a <= L; a += 0.01) {
        double b = (L - a) / 2.0;
        double c = (L - a - b);
        if (c <= 0) continue;
        // if (a + b + c != L) continue;
        if (ans < a * b * c) {
            // printf("a: %.7f, b: %.7f, c: %.7f, cand: %.7f\n", a, b, c, a * b * c);
            ans = a * b * c;
        }
    }

    printf("%.7f\n", ans);

    return 0;
}