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>
using namespace std;
long long mod(long long a) {
  long long c = a % (long long)(1E9 + 7);
  if (c >= 0) return c;
  return c + (long long)(1E9 + 7);
}
long long inf = (long long)1E16;
long long max(long long a, long long b) {
  if (a < b)
    return b;
  else
    return a;
}
long long min(long long a, long long b) {
  if (a > b)
    return b;
  else
    return a;
}
void Max(long long &pos, long long val) { pos = max(pos, val); }
void Min(long long &pos, long long val) { pos = min(pos, val); }
void Add(long long &pos, long long val) { pos = mod(pos + val); }
long double EPS = 1E-12;
template <class T, class S>
inline bool chmax(T &a, S b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T, class S>
inline bool chmin(T &a, S b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
void mod_print(long long k) {
  long long P = 50000;
  for (long long y = 1; y <= P; y++) {
    long long x = mod(y * k);
    if (abs(x) <= P || x + P >= (long long)(1E9 + 7)) {
      if (x + P >= (long long)(1E9 + 7)) {
        x -= (long long)(1E9 + 7);
      }
      cout << x << "/" << y << "\n";
      return;
    }
  }
  cout << "nun"
       << "\n";
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long n;
  cin >> n;
  long long a[n + 1];
  for (long long i = 1; i <= n; i++) cin >> a[i];
  if (n == 1) {
    cout << 1 << " " << 1 << "\n";
    cout << -a[1] << "\n";
    for (long long z = 1; z <= 2; z++) {
      cout << 1 << " " << 1 << "\n";
      cout << 0 << "\n";
    }
    return 0;
  }
  cout << 1 << " " << n << "\n";
  for (long long i = 1; i <= n; i++) {
    cout << -a[i] * n << " ";
  }
  cout << "\n";
  cout << 1 << " " << n - 1 << "\n";
  for (long long i = 1; i <= n - 1; i++) {
    cout << a[i] * (n - 1) << " ";
  }
  cout << "\n";
  cout << n << " " << n << "\n";
  cout << a[n] * (n - 1) << "\n";
  return 0;
}