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*** The hack uses generator ***
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** Command line arguments **
no arguments

** Generated test **
Enter p (probability of picking the missing face when one is known). For equal faces enter 0.5: 

** Generator source **
#include <bits/stdc++.h>
using namespace std;

// Analytical calculation for 2 faces:
// If p is probability to pick the missing face when one face is already found:
// Expected turns = 1 + 1/p

double expected_formula(double p) {
    if (p <= 0.0) return INFINITY;
    return 1.0 + 1.0 / p;
}

// Optional Monte-Carlo simulation to verify the result
double simulate(double p, long long trials = 2000000) {
    std::mt19937_64 rng(123456789);
    std::bernoulli_distribution pickA(1.0 - p); // probability of picking face A
    long long totalTurns = 0;
    for (long long t = 0; t < trials; ++t) {
        bool haveA = false, haveB = false;
        long long turns = 0;
        while (!(haveA && haveB)) {
            ++turns;
            bool chooseA = pickA(rng);
            if (chooseA) haveA = true;
            else haveB = true;
        }
        totalTurns += turns;
    }
    return double(totalTurns) / double(trials);
}

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

    double p; // probability to pick the missing face when one is already collected
    // For the symmetric case (two faces equally likely), p = 0.5
    cout << "Enter p (probability of picking the missing face when one is known). "
            << "For equal faces enter 0.5: ";
    if (!(cin >> p)) return 0;

    cout << fixed << setprecision(10);
    double E = expected_formula(p);
    cout << "Analytical expected turns = " << E << "\n";

    // optional: run a quick simulation to verify (comment out if you don't want it)
    cout << "Run simulation to verify? (y/n): ";
    char c;
    cin >> c;
    if (c == 'y' || c == 'Y') {
        double sim = simulate(p, 500000); // half-million trials by default
        cout << "Simulated average turns = " << sim << " (trials = 500000)\n";
    }
    return 0;
}