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:
#############<------------  Xorcestor_X ---------------->############

from math import *


def is_even(p):
    n=len(p)
    count=0
    for i in range(n):
        index=p.index(i,i,n)
        if i==index:
            pass
        else:
            count+=1
            temp=p[i]
            p[i]=p[index]
            p[index]=temp
    # print(p)
    if count%2==0:
        return True
    else:
        return False



prime=[]

def SieveOfEratosthenes():
    global prime
    prime=[1]*2000010
    prime[1]=0
    p=2
    while p*p<=2000001:
        if prime[p]:
            for i in range(p*p,2000002,p):
                prime[i]=0

lpf=[]

def precompute():
    global lpf
    lpf=[0]*1000001
    for i in range(2,1000001):
        if not lpf[i]:
            for j in range(i,1000001,i):
                if not lpf[j]:
                    lpf[j]=i


def binpow(a,b):
    res=1
    while b>0:
        if b&1:
            res*=a
        a*=a
        b>>=1
    return res


def modpow(a,b,x):
    res=1
    while b>0:
        if b&1:
            res*=a
            res%=x
        a*=a
        a%=x
        b>>=1
    return res

cont=[]

def f(x):
    global cont
    total=0
    for i in cont:
        total+=abs(i-x)
    return total


def bs(uv,low,high,target):
    while low+3<high:
        mid=(low+high)/2
        if uv[mid]<target:
            low=mid
        else:
            high=mid-1
    for i in range(high,low-1,-1):
        if uv[i]<target:
            return i
    return -1


def ternary_search(l,r):
    while r-l>10:
        m1=l+(r-l)/3
        m2=r-(r-l)/3
        f1=f(m1)
        f2=f(m2)
        if f1>f2:
            l=m1
        else:
            r=m2

    mino=f(l)

    for i in range(l,r+1):
        mino=min(mino,f(i))

    return mino





n=int(input())
arr=[int(i) for i in input().split()]
if n==1:
    print("1 1")
    print(-1*arr[0])
    print("1 1")
    print(0)
    print("1 1")
    print(0)
else:
    print(1,n)
    for i in range(n):
        print(-1*n*arr[i],end=" ")
        arr[i]-=n*arr[i]
    print()
    print(1,n-1)
    for i in range(n-1):
        print(-1*arr[i],end=' ')
        arr[i]=0
    print()
    print(2,n)
    for i in range(1,n):
        print(-1*arr[i],end=' ')
        arr[i]=0
    print()