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 PYTHON3):

Solution:
# Author Name: Ajay Meena
# Codeforce : https://codeforces.com/profile/majay1638
import sys
import math
import bisect
import heapq
from bisect import bisect_right
from sys import stdin, stdout

# -------------- INPUT FUNCTIONS ------------------


def get_ints_in_variables(): return map(
    int, sys.stdin.readline().strip().split())


def get_int(): return int(sys.stdin.readline())


def get_ints_in_list(): return list(
    map(int, sys.stdin.readline().strip().split()))
def get_list_of_list(n): return [list(
    map(int, sys.stdin.readline().strip().split())) for _ in range(n)]


def get_string(): return sys.stdin.readline().strip()

# -------------- SOLUTION FUNCTION ------------------


def Solution():
    # Write Your Code Here
    n = get_int()
    arr = get_ints_in_list()
    if n == 1:
        print(1, 1)
        print(-arr[0])
        print(1, 1)
        print(0)
        print(1, 1)
        print(0)
        return

    print(1, n-1)
    for i in range(n-1):
        print(arr[i]*(n-1), end=" ")
        arr[i] = arr[i]*n
    print()
    print(n, n)
    print(arr[n-1]*(n-1))
    arr[n-1] = arr[n-1]*n
    print(1, n)
    for i in range(n):
        print(-arr[i], end=" ")
        arr[i] = 0
    print()


def main():
    # Take input Here and Call solution function
    Solution()


# calling main Function
if __name__ == '__main__':
    main()