#include #include #include #include #include #include #define repeat(i,n) for (int i = 0; (i) < (n); ++(i)) typedef long long ll; template bool setmin(T & l, T const & r) { if (not (r < l)) return false; l = r; return true; } using namespace std; vector sieve_of_eratosthenes(int n) { // enumerate primes in [2,n] with O(n log log n) vector is_prime(n+1, true); is_prime[0] = is_prime[1] = false; for (int i = 2; i*i <= n; ++i) if (is_prime[i]) for (int k = i+i; k <= n; k += i) is_prime[k] = false; vector primes; for (int i = 2; i <= n; ++i) if (is_prime[i]) primes.push_back(i); return primes; } map factors(ll n, vector const & primes) { map result; for (int p : primes) { if (n < p *(ll) p) break; while (n % p == 0) { result[p] += 1; n /= p; } } if (n != 1) result[n] += 1; return result; } const ll inf = 1e18+9; template ll go(ll n, map & ps, map::iterator it, ll acc, F cont) { if (it == ps.end()) { return cont(n, ps, acc); } else { ll p; int cnt; tie(p, cnt) = *it; ++ it; ll ans = inf; repeat (i,cnt+1) { setmin(ans, go(n, ps, it, acc, cont)); ps[p] -= 1; acc *= p; n /= p; } ps[p] += cnt+1; return ans; } } template ll go(ll n, map ps, F cont) { return go(n, ps, ps.begin(), 1, cont); } int main() { ll n; cin >> n; vector primes = sieve_of_eratosthenes(ceil(sqrt(n))); map memo; auto ps = factors(n, primes); ll ans = go(n, ps, [&](ll n, map ps, ll a) { if (not memo.count(n)) { memo[n] = go(n, ps, [&](ll c, map ps, ll b) { return (b - 1) + (c - 1); }); } return (a - 1) + memo[n]; }); cout << ans << ' ' << n-1 << endl; return 0; }