#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <queue>
#include <string>
#include <map>
#include <set>
#include <stack>
#include <tuple>
#include <deque>
#include <array>
#include <numeric>
#include <bitset>
#include <iomanip>
#include <cassert>
#include <chrono>
#include <random>
#include <limits>
#include <iterator>
#include <functional>
#include <sstream>
#include <fstream>
#include <complex>
#include <cstring>
#include <unordered_map>
#include <unordered_set>
using namespace std;

using ll = long long;
constexpr int INF = 1001001001;
constexpr int mod = 1000000007;
// constexpr int mod = 998244353;

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

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

    int M;
    cin >> M;
    vector<double> S(1 << M);
    for(int i = 0; i < 1 << M; ++i) cin >> S[i];

    vector<vector<double>> ans(1 << (M + 1), vector<double>(1 << M, 1));
    for(int k = M - 1; k >= 0; --k){
        for(int i = 0; i < 1 << M; i += 1 << (M - k)){
            for(int j = 0; j < 1 << (M - k - 1); ++j){
                ans[1 << k][i + j] = 0;
                for(int l = 1 << (M - k - 1); l < 1 << (M - k); ++l){
                    double p = S[i + j] * S[i + j] / (S[i + j] * S[i + j] + S[i + l] * S[i + l]);
                    ans[1 << k][i + j] += ans[1 << (k + 1)][i + j] * ans[1 << (k + 1)][i + l] * p;
                }
            }
            for(int j = 1 << (M - k - 1); j < 1 << (M - k); ++j){
                ans[1 << k][i + j] = 0;
                for(int l = 0; l < 1 << (M - k - 1); ++l){
                    double p = S[i + j] * S[i + j] / (S[i + j] * S[i + j] + S[i + l] * S[i + l]);
                    ans[1 << k][i + j] += ans[1 << (k + 1)][i + j] * ans[1 << (k + 1)][i + l] * p;
                }
            }
        }
    }

    for(int state = 1; state < 1 << M; ++state){
        for(int player = 0; player < 1 << M; ++player){
            cout << ans[state][player] << ' ';
        }cout << endl;
    }

    cout << fixed << setprecision(10);
    cout << ans[1][0] << endl;

    return 0;
}