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.lang.*;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.util.*;
import java.math.BigInteger;

public class C {
    //code written by a living bruh moment
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        int t = 1;
        for (int tt = 1; tt <= t; tt++) solver.solve(tt, in, out);
        out.close();
    }

    static class Task {

        public void solve(int tt, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            long[] a = in.nextLonga(n);
            if(n==1){
                out.println(1 + " " + 1);
                out.println(-a[0]);
                out.println(1 + " " + 1);
                out.println(1);
                out.println(1 + " " + 1);
                out.println(-1);
                return;
            }
            //first step take all numbers n-1
            out.println(1 + " " + (n-1));
            ArrayList<Long> mults = new ArrayList<>();
            long curr = n-1;
            for(int i = 0; i<n; i++){
                mults.add(curr);
                curr+=(n-1);
            }
            Collections.reverse(mults);
            for(int i = 0; i<n-1; i++){
                long mod = n-((a[i]%n)+n%n);
                long temp = mults.get((int)mod%n);
                out.print(temp + " ");
                a[i] += temp;
            }
            //sceond step check last number if div
            out.println();
            out.println(n + " " + n);
            out.println(-a[n-1]);
            //third step divide all numbers
            out.println(1 + " " + n);
            for(int i = 0; i<n-1; i++){
                out.print(-a[i] + " ");
            }
            out.print(0);
        }
    }

    static void sort(int[] x) {
        shuffle(x);
        Arrays.sort(x);
    }

    static void sort(long[] x) {
        shuffle(x);
        Arrays.sort(x);
    }

    static void shuffle(int[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            int temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }

    static void shuffle(long[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            long temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

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

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

        public String nextLine() {
            try {
                return reader.readLine();
            } catch (Exception e) {
                e.printStackTrace();
            }
            return null;
        }

        public boolean hasNext() {
            String next = null;
            try {
                next = reader.readLine();
            } catch (Exception e) {
            }
            if (next == null) {
                return false;
            }
            tokenizer = new StringTokenizer(next);
            return true;
        }

        public int[] nextInta(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        public long[] nextLonga(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) a[i] = nextLong();
            return a;
        }

        public int[][] nextIntm(int n, int m) {
            int[][] a = new int[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    a[i][j] = nextInt();
                }
            }
            return a;
        }

        public long[][] nextLongm(int n, int m) {
            long[][] a = new long[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    a[i][j] = nextLong();
                }
            }
            return a;
        }

        public BigInteger nextBigInteger() {
            return new BigInteger(next());
        }
    }
}