#include <iostream>
#include <ostream>
#include <vector>
#include <algorithm>
#include <cmath>

class Matrix: public std::vector<std::vector<double>> {
public:
  // конструкторы
  Matrix () = default;
  Matrix (int n, int m);

  // полуконструкторы
  static Matrix eye(int n, double value = 1.0) {
    Matrix t(n, n);

    for(int i = 0; i < n; ++i)
      t[i][i] = value;

    return t;
  }

  // размеры
  auto sizes() const;

  // операторы
  Matrix operator* (const Matrix& other) const;
  Matrix operator+ (const Matrix& other) const;
  Matrix operator- (const Matrix& other) const;

  // операции
  void add_row_to_row(int n, int m, double factor = 1.0);
  void swap_rows(int n, int m);
  void multiply_row(int n, double factor);

  int find_pivot(int n, double EPS = 1e-07);
  void set_zeros(double EPS = 1e-07);

  // алгебра
  Matrix inverse() const;
  double square_norm() const;

  // input and output
  friend std::ostream& operator<< (std::ostream& os, const Matrix& m);
  friend std::istream& operator>> (std::istream& is, Matrix& m);
};

// конструкторы
Matrix::Matrix(int n, int m):
std::vector<std::vector<double>> (n, std::vector<double> (m, 0)) {}

// размеры
auto Matrix::sizes() const {
  std::pair<int, int> result;

  result.first = static_cast<int>(this->size());
  result.second = static_cast<int>((*this)[0].size());

  return result;
}

// операторы
Matrix Matrix::operator* (const Matrix& other) const {
  // по столбцам a_1_1 ... a_1_n
  // по строкам a_1_1 .. a_m_1
  int m = (this->sizes()).first;
  int n = (this->sizes()).second;

  int other_m = other.sizes().first;
  int other_n = other.sizes().second;

  Matrix t (m, other_n);

  for(int i = 0; i < m; ++i){
    for(int j = 0; j < other_n; ++j){
      for(int k = 0; k < n; ++k)
        t[i][j] += (*this)[i][k] * other[k][j];
    }
  }

  return t;
}

Matrix Matrix::operator+ (const Matrix& other) const {
  if(this->sizes() != other.sizes())
    return Matrix::eye(1);

  Matrix t = *this;

  for(int i = 0; i < t.sizes().first; ++i){
    for(int j = 0; j < t.sizes().second; ++j){
      t[i][j] += other[i][j];
    }
  }

  return t;
}

Matrix Matrix::operator- (const Matrix& other) const {
  if(this->sizes() != other.sizes())
    return Matrix::eye(1);

  Matrix t = *this;

  for(int i = 0; i < t.sizes().first; ++i){
    for(int j = 0; j < t.sizes().second; ++j){
      t[i][j] -= other[i][j];
    }
  }

  return t;
}

// операции
void Matrix::add_row_to_row(int n, int m, double factor){
  for(int j = 0; j < (*this)[0].size(); ++j)
    (*this)[n][j] += factor * (*this)[m][j];
}

void Matrix::swap_rows(int n, int m){
  std::swap((*this)[n], (*this)[m]);
}

void Matrix::multiply_row(int n, double factor){
  for(int j = 0; j < (*this)[0].size(); ++j)
    (*this)[n][j] *= factor;
}

int Matrix::find_pivot(int n, double EPS){
  for(int i = n; i < this->size(); ++i)
    if(std::abs((*this)[i][n]) > EPS)
      return i;

  return -1;
}

void Matrix::set_zeros(double EPS){
  for(auto& i: *this)
    for(auto& j: i)
      if(std::abs(j) < EPS)
        j = 0;
}

// алгебра
Matrix Matrix::inverse() const {
  Matrix t = (*this);
  Matrix inversed = Matrix::eye(t.size());

  for(int i = 0; i < t.size(); ++i){
    int pivot = t.find_pivot(i);

    t.swap_rows(i, pivot);
    inversed.swap_rows(i, pivot);

    double factor = t[i][i];
    t.multiply_row(i, 1.0 / factor);
    inversed.multiply_row(i, 1.0 / factor);

    for(int j = 0; j < t.size(); ++j){
      if(j != i){
        factor = t[j][i];

        t.add_row_to_row(j, i, -factor);
        inversed.add_row_to_row(j, i, -factor);
      }
    }
  }

  return inversed;
}

double Matrix::square_norm() const {
  double norm = 0;

  for(auto&& i: *this){
    for(auto&& j: i){
      norm += j * j;
    }
  }

  return norm;
};

// input and output
std::ostream& operator<< (std::ostream& os, const Matrix& m) {
  for(auto&& i: m){
    for(auto&& j: i){
      os << j << ' ';
    }

    os << '\n';
  }

  return os;
}

std::istream& operator>> (std::istream& is, Matrix& m) {
  for(auto& i: m)
    for(auto& j: i)
      is >> j;

  return is;
}

Matrix generate_matrix(int n){
    if(n < 3)
        return Matrix::eye(n);

    Matrix t(n, n);

    t[0][0] = -1.0;
    t[0][1] = 1.0;

    for(int i = 1; i < n - 1; ++i){
        t[i][i - 1] = 1.0;
        t[i][i] = -2.0;
        t[i][i + 1] = 1.0;
    }

    t[n - 1][n - 2] = 1.0;
    t[n - 1][n - 1] = -((n - 1) * 1.0 / n);

    return t;
}

int main(){
  return 0;
}