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:
import java.io.*;
import java.util.*;
import java.math.*;

public class Main
{
    BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer tokenizer=null;

    public static void main(String[] args) throws IOException
    {
        new Main().execute();
    }

    void debug(Object...os)
    {
        System.out.println(Arrays.deepToString(os));
    }

    int ni() throws IOException
    {
        return Integer.parseInt(ns());
    }

    long nl() throws IOException
    {
        return Long.parseLong(ns());
    }

    double nd() throws IOException
    {
        return Double.parseDouble(ns());
    }

    String ns() throws IOException
    {
        while (tokenizer == null || !tokenizer.hasMoreTokens())
            tokenizer = new StringTokenizer(br.readLine());
        return tokenizer.nextToken();
    }

    String nline() throws IOException
    {
        tokenizer=null;
        return br.readLine();
    }


    //Main Code starts Here
    int totalCases, testnum;


    void execute() throws IOException
    {
//        totalCases = ni();
//        for(testnum = 1; testnum <= totalCases; testnum++)
//        {
//            if(!input())
//                break;
            solve();
//        }
    }

    void solve() throws IOException
    {
        int n = ni();
        long[] arr = nlarr();

        if( n==1 ) {
            System.out.println("1 1");
            System.out.println("0");
            System.out.println("1 1");
            System.out.println("0");
            System.out.println("1 1");
            System.out.println(-arr[0]);
            return;
        }


        System.out.println("1 "+n);
        for( int i=0; i<n; i++) {
            if( i==0 )
                System.out.print((long)-n*(long)arr[i]);
            else
                System.out.print(" " + ((long)(-n)*(long)arr[i]));
        }
        System.out.println();
        System.out.println("2 "+n);
        for( int i=1; i<n; i++) {
            if( i==1 )
                System.out.print((long)(n-1)*(long)arr[i]);
            else
                System.out.print(" " + ((long)(n-1)*(long)arr[i]));
        }

        System.out.println();
        System.out.println("1 1");
        System.out.println(-(long)arr[0]+(long)n*(long)arr[0]);

    }

    boolean input() throws IOException
    {
        return true;
    }

    int[] niarr() throws IOException {
        String str = nline();
        String[] tokens = str.split(" ");
        int[] arr = new int[tokens.length];
        for( int i=0; i<arr.length; i++) {
            arr[i] = Integer.parseInt(tokens[i]);
        }
        return arr;
    }

    long[] nlarr() throws IOException {
        String str = nline();
        String[] tokens = str.split(" ");
        long[] arr = new long[tokens.length];
        for( int i=0; i<arr.length; i++) {
            arr[i] = Long.parseLong(tokens[i]);
        }
        return arr;
    }

    private static void print(int[] arr) {
        for (int a : arr)
            System.out.print(a + ", ");
        System.out.println();
    }

    private static void print(int[][] arr) {
        for (int[] a : arr)
            print(a);
    }

}