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 JAVA):

Solution:

//template
import java.util.*;
import java.util.stream.*;
import java.io.*;
public class Main{
	static BufferedReader in= new BufferedReader(new InputStreamReader(System.in));
	static PrintWriter out= new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
	
	private static final int HUNDRED = 100;
	public static void main(String[] args) throws IOException{
		
		/*System.out.println(MCD(1,4));
		System.out.println(mcm(1,4));
		System.out.println(mcm(5,4));
		*/
		int n=Integer.parseInt(in.readLine());
		int m=n-1;
		long[] a=readLongs();
		if(n>1) {
			out.append("1 "+n+"\n");
			for(int i=0;i<n;i++) {
				out.append(-a[i]*n+" ");
			}
			out.append("\n2 "+n+"\n");
			for(int i=1;i<n;i++) {
				out.append(a[i]*m+" ");
			}
			out.append("\n1 1\n");
			out.append(-a[0]+a[0]*n+"");
		}else {
			out.append("1 1\n"+(-1*a[0])+"\n");
			out.append("1 1\n"+0+"\n");
			out.append("1 1\n"+0+"\n");
		}
		
		out.flush();
		in.close();
		out.close();
	}
	public static int mcm(long num1,long num2) {
		int mcm=1;
		int i=2;
		while(i <= num1 || i <= num2)
        {
            if(num1%i==0 || num2%i==0)
            {
            mcm=mcm*i;
            if(num1%i==0) num1=num1/i;
            if(num2%i==0) num2=num2/i;
            }
            else
                i=i+1;               
        }                       
		return mcm;
	}
	public static long MCD(long a, long b) {
	       if(b==0)
	           return a;
	       else
	           return MCD(b, a % b);
	}
	private static int modulo(int S, int N) { return ((S) & (N - 1)); } // returns S % N, where N is a power of 2
	private static int isPowerOfTwo(int S) { return (S & (S - 1)) == 0 ? 1 : 0; }
	private static int[] readInts() throws IOException {
		return Stream.of(in.readLine().split(" ")).mapToInt(Integer::parseInt).toArray();
	}
	private static int readInt() throws IOException {
		return Integer.parseInt(in.readLine());
	}
	private static long[] readLongs() throws IOException {
		return Stream.of(in.readLine().split(" ")).mapToLong(Long::parseLong).toArray();
	}
	private static long readLong() throws IOException {
		return Long.parseLong(in.readLine());
	}
	 
}