Problem:
Score : 400 points

Problem Statement

Give a pair of integers (A, B) such that A^5-B^5 = X.
It is guaranteed that there exists such a pair for the given integer X.

Constraints

1 \leq X \leq 10^9

X is an integer.

There exists a pair of integers (A, B) satisfying the condition in Problem Statement.

Input

Input is given from Standard Input in the following format:

X

Output

Print A and B, with space in between.
If there are multiple pairs of integers (A, B) satisfying the condition, you may print any of them.

A B

Sample Input 1

33

Sample Output 1

2 -1

For A=2 and B=-1, A^5-B^5 = 33.

Sample Input 2

1

Sample Output 2

0 -1

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)


/*
	@ãƒ»Ï‰ãƒ»@
*/

// Memo:https://scrapbox.io/hitsujirere-memo/

/*****/

/**/
#pragma GCC target("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
/**/

#include <bits/stdc++.h>

//#define int long long

using namespace std;
using ll = long long;
using ld = long double;
using pint = pair<int, int>;
using pll = pair<long long, long long>;
template <class T>
using vec = vector<T>;
template <class T>
using grapth = vec<vec<T>>;

#define rep(i, n) for (ll i = 0, i##_len = (n); i < i##_len; ++i)
#define rep1(i, n) for (ll i = 1, i##_len = (n); i <= i##_len; ++i)
#define rrep(i, n) for (ll i = (n)-1; i >= 0; --i)
#define rrep1(i, n) for (ll i = (n); i > 0; --i)
#define step(i, a, n) for (ll i = (a), i##_len = (a) + (n); i < i##_len; ++i)
#define rstep(i, a, n) for (ll i = (a) + (n)-1, i##_len = (a); i >= i##_len; --i)
#define range(i, a, b) for (ll i = (a), i##_len = (b); i < i##_len; ++i)
#define rrange(i, a, b) for (ll i = (b)-1, i##_len = (a); i >= i##_len; --i)

constexpr int INF = numeric_limits<int>::max();
constexpr ll INFL = numeric_limits<ll>::max();

std::string strMulti(const char c, const int n)
{
    std::string out = "";
    for (int i = 0; i < n; i++)
    {
        out += c;
    }
    return out;
}
std::string strMulti(const std::string t, const int n)
{
    std::string out = "";
    for (int i = 0; i < n; i++)
    {
        out += t;
    }
    return out;
}
std::string tab(const int n)
{
    return strMulti('\t', n);
}
std::string join(const vector<string> &v, const char *delim = 0)
{
    std::string s;
    if (!v.empty())
    {
        s += v[0];
        for (decltype(v.size()) i = 1, c = v.size(); i < c; ++i)
        {
            if (delim)
                s += delim;
            s += v[i];
        }
    }
    return s;
}

string to_string(string &s) { return '"' + s + '"'; }
string to_string(char &c) { return string({'\'', c, '\''}); }
template <class T1, class T2>
string to_string(pair<T1, T2> p)
{
    return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <class Tuple, size_t... I>
string _to_string_tuple(Tuple &&t, std::index_sequence<I...>)
{
    vector<string> texts = {to_string(std::get<I>(t))...};
    return "(" + join(texts, ", ") + ")";
}
template <class... Args>
string to_string(tuple<Args...> t)
{
    using Tuple = tuple<Args...>;
    return _to_string_tuple(std::forward<Tuple>(t),
                            std::make_index_sequence<std::tuple_size<std::decay_t<Tuple>>::value>{});
}
template <class T>
string to_string(vector<T> ar)
{
    vector<string> texts(ar.size());
    for (size_t i = 0; i < ar.size(); ++i)
    {
        texts[i] = to_string(ar[i]);
    }
    return "{" + join(texts, ", ") + "}";
}
template <class T>
string to_string(initializer_list<T> il)
{
    vector<string> texts(il.size());
    size_t i = 0;
    for (T v : il)
    {
        texts[i] = to_string(v);
        i++;
    }
    return "{" + join(texts, ", ") + "}";
}

#ifdef DEBUG_BUILD
#define debugvar(x) debugln(#x, (x))
#define debugvartab(x, t) debugln(tab(t) + #x, (x))
void debug(string name)
{
    std::cerr << name;
}
void debugln(string name)
{
    std::cerr << name << '\n';
}
template <class T>
void debug(string name, T v)
{
    std::cerr << name << " = " << to_string(v);
}
template <class T>
void debugln(string name, T v)
{
    std::cerr << name << " = " << to_string(v) << '\n';
}
template <class T>
void debug(string name, initializer_list<T> il)
{
    std::cerr << name << " = " << to_string(il);
}
template <class T>
void debugln(string name, initializer_list<T> il)
{
    std::cerr << name << " = " << to_string(il) << '\n';
}
template <class... Args>
void debug(string name, Args... args)
{
    std::cerr << name << " = " << to_string(tuple<Args...>(args...));
}
template <class... Args>
void debugln(string name, Args... args)
{
    std::cerr << name << " = " << to_string(tuple<Args...>(args...)) << '\n';
}
#else
#define debugvar(x)
#define debugvartab(x, t)
void debug(string name)
{
}
void debugln(string name) {}
template <class T>
void debug(string name, T v) {}
template <class T>
void debugln(string name, T v) {}
template <class T>
void debug(string name, initializer_list<T> il) {}
template <class T>
void debugln(string name, initializer_list<T> il) {}
template <class... Args>
void debug(string name, Args... args) {}
template <class... Args>
void debugln(string name, Args... args) {}
#endif

#define all(x) (x).begin(), (x).end()
#define pair(a, b) make_pair(a, b)

template <class T>
bool chmax(T &a, const T b)
{
    if (a < b)
    {
        a = b;
        return true;
    }
    return false;
}
template <class T>
bool chmin(T &a, const T b)
{
    if (a > b)
    {
        a = b;
        return true;
    }
    return false;
}
template <class T>
T divup(const T a, const T b)
{
    if (a % b == 0)
    {
        return a / b;
    }
    return a / b + 1;
}
template <class T>
bool cmp_2nd(pair<T, T> a, pair<T, T> b)
{
    if (a.second != b.second)
    {
        return a.second < b.second;
    }
    return a.first < b.first;
}
ll modpow(ll x, ll n, const ll &p)
{
    ll ret = 1;
    while (n > 0)
    {
        if (n & 1)
        {
            (ret *= x) %= p;
        }
        (x *= x) %= p;
        n >>= 1;
    }
    return ret;
}
template <class T>
T modinv(T a, const T &p)
{
    T b = p, u = 1, v = 0;
    while (b)
    {
        T t = a / b;
        a -= t * b;
        swap(a, b);
        u -= t * v;
        swap(u, v);
    }
    u %= p;
    if (u < 0)
    {
        u += p;
    }
    return u;
}
template <class T>
T math_P(T m, T n)
{
    T ret = 1;
    for (T i = m; i > m - n; i--)
    {
        ret *= i;
    }
    return ret;
}
template <class T>
T math_C(T m, T n)
{
    T ret = math_P(m, n);
    for (T i = 2; i <= n; i++)
    {
        ret /= i;
    }
    return ret;
}
ll extended_euclidean(ll u, ll v)
{
    ll r0 = u;
    ll r1 = v;
    ll s0 = 1;
    ll s1 = 0;
    ll t0 = 0;
    ll t1 = 1;
    while (r1 != 0)
    {
        ll q = r0 / r1;
        ll r = r0 - q * r1;
        ll s = s0 - q * s1;
        ll t = t0 - q * t1;
        r0 = r1;
        s0 = s1;
        t0 = t1;
        r1 = r;
        s1 = s;
        t1 = t;
    }
    if (t0 < 0)
    {
        return t0 + u;
    }
    else
    {
        return t0;
    }
}
ll math_C_mod(ll n, ll c, const ll &p)
{
    ll upe = 1;
    ll dow = 1;
    for (ll i = 1; i < c + 1; ++i)
    {
        upe = upe * n % p;
        dow = dow * i % p;
        n -= 1;
    }
    return (upe * extended_euclidean(p, dow)) % p;
}
template <class T>
T math_gcd(T a, T b)
{
    if (b == 0)
    {
        return a;
    }
    else
    {
        return math_gcd(b, a % b);
    }
}
template <class T>
T math_lcm(T a, T b) { return a / math_gcd(a, b) * b; }
template <class T>
T SumStep(T a, T n, T d) { return n * (2 * a + (n - 1) * d) / 2; }
template <class T>
T SumRange(T a, T b, T d) { return SumStep(a, (b - a) / d, d); }

constexpr ll MOD = 1000000007; // 10^9+7

/*****/

// 約数列挙
template <class T>
vector<T> enum_divisors(T n)
{
    vector<T> res;
    for (T i = 1; i * i <= n; ++i)
    {
        if (n % i == 0)
        {
            res.push_back(i);
            if (n != i * i)
                res.push_back(n / i);
        }
    }
    sort(res.begin(), res.end(), greater<ll>());
    return res;
}

ll solve(ll A, ll B)
{
    return A * A * A * A * A - B * B * B * B * B;
}

void Main()
{
    ll X;
    cin >> X;
    auto XD = enum_divisors(X);

    for (auto d : XD)
    {
        debugvar(d);

        for (ll A = X / d;; --A)
        {
            ll B = A - d;
            if (solve(A, B) == X)
            {
                cout << A << " " << B << endl;
                return;
            }

            if (solve(A, B) < X)
            {
                break;
            }
        }
    }
}

/*****/

int main()
{
    std::ios::sync_with_stdio(false);
    std::cin.tie(0);

    std::cout << std::fixed << std::setprecision(10);

#ifdef DEBUG_BUILD
    while (true)
    {
        Main();
        std::cerr << flush;
        std::cout << "-----" << endl;
    }
#else
    Main();
    std::cerr << flush;
    std::cout << flush;
#endif

    return 0;
}