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.awt.*;
import java.io.*;

import java.math.BigInteger;
import java.util.*;

public class TaskC {


    static class Edge implements Comparable<Edge> {
        int v,cost;


        public Edge( int x, int y) {
            this.v = x;
            this.cost = y;
        }

        public int compareTo(Edge o) {
            if (cost  == o.cost)
                return v - o.v;
            return v - o.v;
        }

        @Override
        public boolean equals(Object o) {
            Edge edge = (Edge) o;
            return v == edge.v &&
                    cost == edge.cost;
        }


        public String toString() {
            return  v+" "+ cost;
        }
    }
    static long sum = 0;
    static ArrayList<Edge>[]adjList;
    static int reaches;
    static boolean[]vis;
    static HashSet<Integer> set;


    static char[][] grid;
    static int R, C;
    static int[] dx = new int[]{-1, 1, 0, 0};
    static int[] dy = new int[]{0, 0, -1, 1};
    static boolean[]visited;


    static boolean valid(int i, int j , int R1 , int C1)
    {
        return i != -1 && j != -1 && i != R1 && j != C1;
    }



    static Queue<Point> bfs(int n, int m , int s1 , int s2)
    {
        Queue<Point> q = new LinkedList<Point>();
        q.add(new Point(s1 , s2));
        boolean visited [][] = new boolean[n][m];
        visited[s1][s2] = true;
        Queue<Point> ans = new LinkedList<>();
        while(!q.isEmpty())
        {
            Point p = q.poll();
            ans.add(p);
            for (int i = 0 ; i < dx.length; i++)
            {
                int x = p.x + dx[i], y = p.y + dy[i];
                if(valid(x , y , n , m) && !visited[x][y])
                {
                    visited[x][y] = true;
                    q.add(new Point(x,y));

                }
            }

        }
        return ans;
    }



    public static void main(String[] args) throws Exception {

        Scanner sc = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);

        int n = sc.nextInt();
        int[]arr = new int[n];

        for (int i =  0;i < n ;i++) arr[i] = sc.nextInt();

        if(n == 1)
        {
            pw.println("1 1");
            pw.println(-arr[0]);
            pw.println("1 1");
            pw.println(0);
            pw.println("1 1");
            pw.println(0);

        }
        else
        {
            pw.println("1 1");
            pw.println((-arr[0]));
            arr[0] = 0;
            pw.println("1 "+n);
            for (int  i = 0 ; i < n ; i++)
                pw.print(1l* -arr[i]*n+ " ");

            pw.println();

            pw.println("2 "+n);
            for (int i = 1 ; i < n ; i++)
                pw.print(1l * arr[i]*(n-1)+" ");


        }


        pw.close();
    }
    static class Point implements Comparable<Point>
    {
        int x ,y ;

        public Point(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public int compareTo(Point o) {
            if (x == o.x) {
                return y - o.y;
            }
            return x - o.x;
        }

        @Override
        public String toString() {
            return "Point{" +
                    "x=" + x +
                    ", y=" + y +
                    '}';
        }
    }

    static class Circle implements Comparable<Circle>
    {
        int x , radius;
        public Circle(int x , int r)
        {
            this.x = x;
            this.radius = r;
        }

        public boolean isInside(Point p)
        {
            return Math.sqrt((p.x - x)*(p.x - x) + (p.y)*(p.y)) <= radius;
        }

        @Override
        public String toString() {
            return "Circle{" +
                    "x=" + x +
                    ", radius=" + radius +
                    '}';
        }

        @Override
        public int compareTo(Circle o) {
            return x - o.x;
        }
    }

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

    static long lcm(int a, int b)
    {
        return (a*b)/gcd(a, b);
    }


    private  static int dis(int xa , int ya , int xb , int yb)
    {
        return (xa-xb)*(xa - xb) + (ya- yb)*(ya-yb);
    }


    static class Pair implements Comparable<Pair> {
        int x,y;


        public Pair(int x, int y) {
            this.x = x;
            this.y = y;
        }

        public int compareTo(Pair o) {
            if (y  == o.y)
                return x - o.x;
            return y - o.y;

        }

        public double dis(Pair a){

            return (a.x - x)*(a.x - x) + (a.y-y)*(a.y-y);
        }

        public String toString() {
            return  x+" "+ y;
        }
        public boolean overlap(Pair a)
        {
            if((this.x >= a.x && this.x <= a.y) || (a.x >= this.x && a.x <= this.y)) return true;
            return false;

        }
    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

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

        public boolean check() {
            if (!st.hasMoreTokens())
                return false;
            return true;
        }

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

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

        public String nextLine() {
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException(e);
            }
        }

        public double nextDouble() {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++)
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec)
                        f *= 10;
                }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }

        public boolean ready() {
            try {
                return br.ready();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
    }
}