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.*;

public class C {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    static FastReader s = new FastReader();
    static PrintWriter out = new PrintWriter(System.out);

    private static int[] rai(int n) {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextInt();
        }
        return arr;
    }

    private static int[][] rai(int n, int m) {
        int[][] arr = new int[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                arr[i][j] = s.nextInt();
            }
        }
        return arr;
    }

    private static long[] ral(int n) {
        long[] arr = new long[n];
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextLong();
        }
        return arr;
    }

    private static long[][] ral(int n, int m) {
        long[][] arr = new long[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                arr[i][j] = s.nextLong();
            }
        }
        return arr;
    }

    private static int ri() {
        return s.nextInt();
    }

    private static long rl() {
        return s.nextLong();
    }

    private static String rs() {
        return s.next();
    }

    static int gcd(int a,int b)
    {
        if(b==0)
        {
            return a;
        }
        return gcd(b,a%b);
    }

    static boolean isPrime(int n) {
        //check if n is a multiple of 2
        if (n % 2 == 0) return false;
        //if not, then just check the odds
        for (int i = 3; i <= Math.sqrt(n); i += 2) {
            if (n % i == 0)
                return false;
        }
        return true;
    }
    public static void main(String[] args) {
        StringBuilder ans = new StringBuilder();
//        int t = ri();
        int t = 1;
        while (t-- > 0){
            int n=ri();
            long[] arr=ral(n);
            if(n==1)
            {
                long val=arr[0];
                ans.append("1 1\n");
                ans.append("0").append("\n");


                ans.append("1 1\n");
                ans.append("0").append("\n");



                ans.append("1 1\n");
                if(val==0)
                {
                    ans.append("0").append("\n");
                }
                else {
                    ans.append(-val).append("\n");
                }
                continue;
            }
            else if(n==2)
            {
                ans.append("1 1\n");
                if(arr[0]==0)
                {
                    ans.append("0").append("\n");
                }
                else {
                    ans.append(-arr[0]).append("\n");
                }

                ans.append("2 2\n");
                ans.append("0").append("\n");

                ans.append("2 2\n");
                if(arr[1]==0) {
                    ans.append("0").append("\n");
                }
                else {
                    ans.append(-arr[1]).append("\n");
                }
                continue;
            }
            else if(n==3)
            {
                ans.append("1 1\n");
                if(arr[0]==0)
                {
                    ans.append("0").append("\n");
                }
                else {
                    ans.append(-arr[0]).append("\n");
                }

                ans.append("2 2\n");
                if(arr[1]==0)
                {
                    ans.append("0").append("\n");
                }
                else {
                    ans.append(-arr[1]).append("\n");
                }

                ans.append("3 3\n");
                if(arr[2]==0)
                {
                    ans.append("0").append("\n");
                }
                else {
                    ans.append(-arr[2]).append("\n");
                }
                continue;
            }

            //first
            ans.append("1 ").append(n-1).append("\n");
            for(int i=0;i<n-1;i++)
            {
                long mod= (arr[i]%n);
//                if(mod<0)
//                {
//                    mod+=n;
//                }
//                if(mod==0)
//                {
//                    ans.append("0 ");
//                    continue;
//                }

                ans.append(((long)n-1)*mod).append(" ");
                arr[i]+=((long)n-1)*mod;
            }
            ans.append("\n");

            //second
            ans.append(n).append(" ").append(n).append("\n");
            ans.append(-arr[n-1]).append("\n");
            arr[n-1]=0;


            //third
            ans.append("1 ").append(n).append("\n");
            for(int i=0;i<n;i++)
            {
                if(arr[i]==0)
                {
                    ans.append("0 ");
                }
                else {
                    ans.append(-arr[i]).append(" ");
                }
            }
            ans.append("\n");
        }

        out.print(ans.toString());
        out.flush();

    }


}