#define _CRT_SECURE_NO_WARNINGS
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
//#define endl '\n'
#define boostIO() ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
ll gcd(ll a, ll b) { return (b == 0 ? a : gcd(b, a % b)); }
typedef long double ld;
typedef vector<vector<ld>> matrix;

matrix mul(const matrix& a, const matrix& b) {
    matrix ans(a.size(), vector<ld>(b[0].size()));
    for (int i = 0; i < a.size(); ++i)
        for (int j = 0; j < b[0].size(); ++j)
            for (int k = 0; k < b.size(); ++k)
                ans[i][j] += a[i][k] * b[k][j];

    return ans;
}
void print(string name,const matrix& a) {
    cout << name << " = \n";
    for (auto row : a) {
        for (auto x : row) {
            cout << fixed << setw(15) << x;
        }
        cout << endl;
    }
}

int main() {

    matrix A = {
        {352809.0 / 50000,-233253.0 / 100000.0,-662893.0 / 100000.0,406369.0 / 50000.0,-518723.0 / 100000.0},
        {65007.0 / 10000.0,-281899.0 / 100000.0,-451277.0 / 100000.0,-27897.0 / 10000.0,906247.0 / 100000.0},
        {-787103.0 / 100000,17213.0 / 2000,75103.0 / 10000,855647.0 / 100000.0,-614673.0 / 100000.0},
        {15981.0 / 5000.0,-210577.0 / 10000000.0,26733.0 / 4000.0,-493469.0 / 50000.0,31539.0 / 6250.0},
        {177343.0 / 100000.0,-453597.0 / 100000,-187841.0 / 100000,93833.0 / 12500.0,-417783.0 / 50000.0}
    };
    matrix b = { {2.23609}, {-8.3874}, {-2.47353}, {7.43828}, {-0.746177} };
    print("A", A);
    matrix L = {
        {1,0,0,0,0},
        {36115.0 / 39201,1,0,0,0},
        {-787103.0 / 705618,-15692444283.0 / 1751193736,1,0,0},
        {53270.0 / 117603,-135308249341.0 / 87559686800,1436157077576729763.0 / 1702456511488374550,1,0},
        {177343.0 / 705618,10322237821.0 / 1751193736,-22718846198335381.0 / 34049130229767491.0,1572772953187969223765.0 / 3211649824104307778373.0,1}
    };
    print("L", L);
    matrix U = {
        {352809.0 / 50000,-233253.0 / 100000,-662893.0 / 100000,406369.0 / 50000,-518723.0 / 100000},
        {0,-218899217.0 / 326675000,3124935509.0 / 1960050000,-251799599.0 / 24500625,1695608431.0 / 122503125},
        {0,0,34049130229767491.0 / 2364111543600000,-176060634498793.0 / 2364111543600,26501529123999967.0 / 236411154360000},
        {0,0,0,9634949472312923335119.0 / 288551951099724500000.0,-379615477841909321289209.0 / 5771039021994490000000.0},
        {0,0,0,0,118003540165276470656138483873.0 / 6423299648208615556746000000.0}
    };
    print("U", U);
    auto A2 = mul(L, U);
    print("A2", A2);
    matrix y(5, vector<ld>(1));
    for (int i = 0; i < 5; ++i) {
        ld sum = 0;
        for (int j = 0; j < i; ++j)
            sum += L[i][j] * y[j][0];
        y[i][0] = (b[i][0] - sum) / L[i][i];
    }
    print("y", y);
    print("L * y", mul(L, y));

    matrix x(5, vector<ld>(1));
    for (int i = 4; i >= 0; --i) {
        ld sum = 0;
        for (int j = i + 1; j < 5; ++j) {
            sum += U[i][j] * x[j][0];
        }
        x[i][0] = (y[i][0] - sum) / U[i][i];
    }
    print("x", x);
    print("A * x", mul(A, x));
}