#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;
    }
}

const ld EPS = 1e-6;
const ld INF = LONG_MAX;

int gauss(matrix& a, vector<ld>& ans) {
    int n = (int)a.size();
    int m = (int)a[0].size() - 1;

    vector<int> where(m, -1);
    for (int col = 0, row = 0; col < m && row < n; ++col) {
        int sel = row;
        for (int i = row; i < n; ++i)
            if (abs(a[i][col]) > abs(a[sel][col]))
                sel = i;
        if (abs(a[sel][col]) < EPS)
            continue;
        for (int i = col; i <= m; ++i)
            swap(a[sel][i], a[row][i]);
        where[col] = row;

        for (int i = 0; i < n; ++i)
            if (i != row) {
                double c = a[i][col] / a[row][col];
                for (int j = col; j <= m; ++j)
                    a[i][j] -= a[row][j] * c;
            }
        ++row;
    }
    print("a", a);
    ans.assign(m, 0);

    for (int i = 0; i < m; ++i)
        if (where[i] != -1)
            ans[i] = a[where[i]][m] / a[where[i]][i];
    for (int i = 0; i < n; ++i) {
        double sum = 0;
        for (int j = 0; j < m; ++j)
            sum += ans[j] * a[i][j];
        if (abs(sum - a[i][m]) > EPS)
            return 0;
    }

    for (int i = 0; i < m; ++i)
        if (where[i] == -1)
            return INF;
    return 1;
}


int main() {

    matrix A = {
        {352809.0 / 50000,-233253.0 / 100000.0,0,0,0},
        {65007.0 / 10000.0,-281899.0 / 100000.0,-451277.0 / 100000.0,0,0},
        {0,17213.0 / 2000,75103.0 / 10000,855647.0 / 100000.0,0},
        {0,0,26733.0 / 4000.0,-493469.0 / 50000.0,31539.0 / 6250.0},
        {0,0,0,93833.0 / 12500.0,-417783.0 / 50000.0}
    };
    vector<ld> b = { 2.23609, -8.3874, -2.47353, 7.43828, -0.746177};
    vector<ld> fi(5), l(5), x(5);
    fi[0] = -A[0][1] / A[0][0];
    l[0] = b[0] / A[0][0];
    for (int i = 1; i < 5; ++i) {
        if (i != 4)
            fi[i] = -A[i][i + 1] /
            (A[i][i] + A[i][i - 1] * fi[i - 1]);

        l[i] = (b[i] - A[i][i - 1] * l[i - 1]) /
            (A[i][i] + A[i][i - 1] * fi[i - 1]);
    }
    x[4] = l[4];
    for (int i = 3; i >= 0; --i) {
        x[i] = x[i + 1] * fi[i] + l[i];
    }
    cout << endl << "fi: \n";
    for (auto x : fi) {
        cout << x << endl;
    }
    cout << endl << "la: \n";
    for (auto x : l) {
        cout << x << endl;
    }
    cout << endl << "X: \n";
    for (auto xx : x) {
        cout << xx << endl;
    }
    matrix X(5, vector<ld>(1));
    for (int i = 0; i < 5; ++i)
        X[i][0] = x[i];
    print("b", mul(A, X));
}