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:
import sys

cases = False

# Pre-defined function
# Begin
def c2(n):
    return n * (n-1) // 2

def get():
    return list(map(int, input().split()))

def bits(n: int):
    return list(bin(n)).count('1')

def main(test_case = False):
    n = int(input()) if test_case else 1
    for _ in range(n):
        test()

def flush():
    sys.stdout.flush()

def parr(arr):
    print(*arr, sep=' ')

def gcd(a, b):
    while b:
        if b % a == 0:
            break
        tmp = a
        a = b % a
        b = tmp
    return a
# End

def ext_gcd(a: int, b: int):
    if (b == 0):
        return [a, [1, 0]]
 
    res = ext_gcd(b, a % b)
    g = res[0]
    x1 = res[1][0]
    y1 = res[1][1]
    x = y1
    y = x1 - y1 * (a // b)
 
    return [g, [x, y]]

def test():
    n = int(input())
    a = get()

    if n == 1:
        print(1, 1)
        print(0)
        print(1, 1)
        print(0)
        print(1, 1)
        print(-a[0])
        return

    print(1, 1)
    print(-a[0])
    a[0] = 0

    k = ext_gcd(n, n-1)
    print(2, n)
    for i in range(n-1):
        temp = -k[1][1] * a[i+1] * (n-1)
        a[i+1] += temp
        print(temp, end=' ')
    print('')
    
    print(1, n)
    for i in range(n):
        print(-a[i], ' ')

main(cases)