Problem: You are given an array a of n integers.

You want to make all elements of a equal to zero by doing the following operation exactly three times:

  * Select a segment, for each number in this segment we can add a multiple of len to it, where len is the length of this segment (added integers can be different). 



It can be proven that it is always possible to make all elements of a equal to zero.

Input

The first line contains one integer n (1 ≤ n ≤ 100 000): the number of elements of the array.

The second line contains n elements of an array a separated by spaces: a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9).

Output

The output should contain six lines representing three operations.

For each operation, print two lines:

  * The first line contains two integers l, r (1 ≤ l ≤ r ≤ n): the bounds of the selected segment.

  * The second line contains r-l+1 integers b_l, b_{l+1}, ..., b_r (-10^{18} ≤ b_i ≤ 10^{18}): the numbers to add to a_l, a_{l+1}, …, a_r, respectively; b_i should be divisible by r - l + 1.

Example

Input


4
1 3 2 4


Output


1 1 
-1
3 4
4 2
2 4
-3 -6 -6

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#pragma GCC optimize "trapv"
using namespace std;
void huehue(istream_iterator<string> it) {}
template <typename T, typename... Args>
void huehue(istream_iterator<string> it, T a, Args... args) {
  cout << *it << " = " << a << ", ";
  huehue(++it, args...);
}
template <class T>
T inf() {
  return numeric_limits<T>::max();
}
void read() { return; }
void print() { return; }
void println() {
  cout << "\n";
  return;
}
template <class T>
T read(T &x) {
  cin >> x;
  return x;
}
template <class T>
void print(T a) {
  cout << a;
}
template <class T>
void println(T a) {
  cout << a << "\n";
}
template <class T>
void read(vector<T> &arr) {
  for (auto &i : arr) cin >> (i);
}
template <class T>
void print(vector<T> arr) {
  for (auto &i : arr) {
    cout << i << " ";
  }
}
template <class T>
void println(vector<T> arr) {
  for (auto &i : arr) {
    cout << i << " ";
  }
  cout << "\n";
}
template <class T>
void read(vector<vector<T>> &arr) {
  for (auto &i : arr) read(i);
}
template <class T>
void print(vector<vector<T>> arr) {
  for (auto &i : arr) println(i);
}
template <class T>
void println(vector<vector<T>> arr) {
  for (auto &i : arr) println(i);
}
template <typename T, typename... Args>
void read(vector<T> &arr, Args &...args) {
  read(arr);
  read(args...);
}
template <typename T, typename... Args>
void read(vector<vector<T>> &arr, Args &...args) {
  read(arr);
  read(args...);
}
template <typename T, typename... Args>
void read(T &a, Args &...args) {
  cin >> (a);
  read(args...);
}
template <typename T, typename... Args>
void print(vector<T> &arr, Args &...args) {
  print(arr);
  print(args...);
}
template <typename T, typename... Args>
void print(T a, Args... args) {
  cout << a << " ";
  print(args...);
};
template <typename T, typename... Args>
void println(vector<T> &arr, Args &...args) {
  print(arr);
  println(args...);
}
template <typename T, typename... Args>
void println(T a, Args... args) {
  cout << a << " ";
  println(args...);
};
const long long int d4i[4] = {-1, 0, 1, 0}, d4j[4] = {0, 1, 0, -1};
const long long int d8i[8] = {-1, -1, 0, 1, 1, 1, 0, -1},
                    d8j[8] = {0, 1, 1, 1, 0, -1, -1, -1};
void solveEachTest(long long int _TestCase = 1) {
  long long int n;
  read(n);
  vector<long long int> arr(n);
  read(arr);
  if (n == 1) {
    println(1, 1);
    println(-arr[0]);
    println(1, 1);
    println(0);
    println(1, 1);
    println(0);
    return;
  }
  println(1, 1);
  for (auto i = (0); (((1) > 0) ? (i) < (1) : (i) > (1)); (i) += (1)) {
    cout << -arr[i] << " ";
    arr[i] = 0;
  }
  println();
  println(2, n);
  for (auto i = (1); (((1) > 0) ? (i) < (n) : (i) > (n)); (i) += (1)) {
    cout << (n - 1) * arr[i] << " ";
    arr[i] += (arr[i] * (n - 1));
  }
  println();
  println(1, n);
  for (auto i = (0); (((1) > 0) ? (i) < (n) : (i) > (n)); (i) += (1)) {
    cout << -arr[i] << " ";
  }
  cout << "\n";
  return;
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.precision(10);
  cout << fixed;
  long long int T3X0 = 0, T353 = 1;
  solveEachTest(T353 - T3X0);
  return 0;
}