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:
#!/usr/bin/env python3
# encoding: utf-8



#----------
# Constants
#----------



#----------
# Functions
#----------

# The function that solves the task
def calc(nums):
    if len(nums) == 1:
        return [ { 'r': (1, 1), 'seq': [ -nums[0] ] }, { 'r': (1, 1), 'seq': [ 0 ] }, { 'r': (1, 1), 'seq': [ 0 ] } ]
    res = list()
    res.append({ 'r': (1, 1), 'seq': [-nums[0]] })
    nums[0] = 0

    n = len(nums)
    m = n - 1
    adds = list()
    for i in range(1, n):
        add = (nums[i] % n) * m
        adds.append(add)
        nums[i] += add

    res.append({ 'r': (2, n), 'seq': adds })
    res.append({ 'r': (1, n), 'seq': [ -num for num in nums] })

    return res

# Reads a string from stdin, splits it by space chars, converts each
# substring to int, adds it to a list and returns the list as a result.
def get_ints():
    return [ int(n) for n in input().split() ]


# Reads a string from stdin, splits it by space chars, converts each substring
# to floating point number, adds it to a list and returns the list as a result.
def get_floats():
    return [ float(n) for n in input().split() ]


# Converts a sequence to the space separated string
def seq2str(seq):
    return ' '.join(str(item) for item in seq)


#----------
# Execution start point
#----------

if __name__ == "__main__":
    zzz = get_ints()
    assert len(zzz) == 1
    n = zzz[0]

    zzz = get_ints()
    assert len(zzz) == n
    nums = zzz

    res = calc(nums)
    for op in res:
        print(op['r'][0], op['r'][1])
        print(seq2str(op['seq']))