euler 45

#include <iostream>
#include <cmath>
using namespace std;

inline constexpr int64_t pentagonal(const int &n) {
    return n * (3 * n - 1LL) >> 1;
}
inline constexpr int64_t hexagonal(const int &n) {
    return n * (2 * n - 1LL);
}
bool isTriagonal(const int64_t &n) {
    const int s = sqrt(n << 1);
    return n << 1 == s * (s + 1LL);
}
bool isPentagonal(const int64_t &n) {
    const int s = sqrt(n * 2 / 3);
    return n == pentagonal(s) || n == pentagonal(s + 1) || n == pentagonal(s + 2) || n == pentagonal(s - 1) || n == pentagonal(s - 2);
}

signed main() {
    ios::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    int i = 144;
    while (!isPentagonal(hexagonal(i)) || !isTriagonal(hexagonal(i))) ++i;
    cout << hexagonal(i);
}