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;
const long long maxs = 1e5 + 3;
const long long maxs1 = 1e3 + 4;
const long long mod = 1e9 + 7;
inline long long add(long long a, long long b) { return (mod + a + b) % mod; }
inline long long sub(long long a, long long b) { return (a - b + mod) % mod; }
inline long long mul(long long a, long long b) { return (1ll * a * b) % mod; }
long long fastpow(long long x, long long y) {
  long long res = 1;
  x = x % mod;
  while (y > 0) {
    if (y & 1) res = (res * x) % mod;
    y = y >> 1;
    x = (x * x) % mod;
  }
  return res;
}
long long inv(long long x) { return fastpow(x, mod - 2); }
bool isPrime(long long n) {
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 || n % 3 == 0) return false;
  for (int i = 5; i * i <= n; i = i + 6)
    if (n % i == 0 || n % (i + 2) == 0) return false;
  return true;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long n;
  cin >> n;
  long long arr[n];
  for (int i = 0; i < n; i++) cin >> arr[i];
  if (n == 1) {
    cout << 1 << " " << 1 << endl;
    cout << -arr[0] << endl;
    cout << 1 << " " << 1 << endl;
    cout << 0 << endl;
    cout << 1 << " " << 1 << endl;
    cout << 0 << endl;
    return 0;
  }
  cout << 1 << " " << 1 << endl;
  cout << (n - 1) * arr[0] << endl;
  cout << 2 << " " << n << endl;
  for (int i = 1; i < n; i++) {
    cout << (n - 1) * arr[i] << " ";
  }
  cout << endl;
  cout << 1 << " " << n << endl;
  for (int i = 0; i < n; i++) {
    cout << -(n)*arr[i] << " ";
  }
}