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

public class problemC {
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        OutputWriter out = new OutputWriter(System.out); // quick fix
        Graph solver = new Graph();
        solver.solve(in, out);
        out.close();

    }

    static class Graph {
        boolean[] visited;
        ArrayList<Integer>[] adjList;
        final long MOD = 1000000007;
        int[] order;
        int[] orderFreq;

        public void solve(InputReader in, OutputWriter out) {

            int n = in.nextInt();
            if (n == 1) {
                out.printf("1 1\n0\n");
                out.printf("1 1\n0\n");
                out.printf("1 1\n%d\n", -in.nextInt());
                return;
            }
            long[] arr = new long[n];
            long[] modL = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = in.nextInt();
                modL[i] = arr[i] % n;
            }
            long op1 = n - 1;
            long[] inOp1 = new long[n - 1];
            for (int i = 0; i < n - 1; i++) {
                long needMod = n - modL[i];
                inOp1[i] = (n - needMod) * (n - 1);
                arr[i] += inOp1[i];
            }
            long op2 = n - modL[n - 1];
            arr[n - 1] += op2;
            out.printf("%d %d\n", 1, n - 1);
            for (int i = 0; i < n - 1; i++) {
                out.printf("%d ", inOp1[i]);
            }
            out.printf("\n%d %d\n%d", n, n, op2);
            out.printf("\n%d %d\n", 1, n);
            for (int i = 0; i < n; i++) {
                out.printf("%d ", -arr[i]);
            }


        }

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

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


        private void initAdjList(int n) {
            adjList = new ArrayList[n];
            visited = new boolean[n];
            for (int i = 0; i < n; i++) {
                adjList[i] = new ArrayList<>();
            }
        }

        class Edge {
            int weight;
            int node;

            public Edge(int node, int weight) {
                this.node = node;
                this.weight = weight;
            }
        }

        class Pair {
            String name;
            int score;

            public Pair(String name, int score) {
                this.name = name;
                this.score = score;
            }
        }

        private int dfs(int u) {
            visited[u] = true;
            if (adjList[u].size() <= 1) {
                return 0;
            }
            int order = Integer.MAX_VALUE;
            for (int v : adjList[u]) {
                if (!visited[v]) {
                    order = Math.min(dfs(v) + 1, order);
                }
            }
            return order;
        }

//        private void bfs(int s) {
//            Queue<Integer> q = new LinkedList<Integer>();
//            q.add(s);
//            visited[s] = true;
//            while(!q.isEmpty()) {
//                int u = q.remove();
//                for(int v: adjList[u]){
//                    if(!visited[v]) {
//                        visited[v] = true;
//                        q.add(v);
//                    }
//                }
//
//            }
//        }

        private int[] nextAInt(int n, InputReader in) {
            int arr[] = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = in.nextInt();
            }
            return arr;
        }

        private long[] nextALong(int n, InputReader in) {
            long arr[] = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = in.nextInt();
            }
            return arr;
        }

    }


    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1 << 16];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (this.numChars == -1) {
                throw new InputMismatchException();
            } else {
                if (this.curChar >= this.numChars) {
                    this.curChar = 0;

                    try {
                        this.numChars = this.stream.read(this.buf);
                    } catch (IOException var2) {
                        throw new InputMismatchException();
                    }

                    if (this.numChars <= 0) {
                        return -1;
                    }
                }

                return this.buf[this.curChar++];
            }
        }

        public int nextInt() {
            int c;
            for (c = this.read(); isSpaceChar(c); c = this.read()) {
                ;
            }

            byte sgn = 1;
            if (c == 45) {
                sgn = -1;
                c = this.read();
            }

            int res = 0;

            while (c >= 48 && c <= 57) {
                res *= 10;
                res += c - 48;
                c = this.read();
                if (isSpaceChar(c)) {
                    return res * sgn;
                }
            }

            throw new InputMismatchException();
        }

        public String next() {
            int c;
            while (isSpaceChar(c = this.read())) {
                ;
            }

            StringBuilder result = new StringBuilder();
            result.appendCodePoint(c);

            while (!isSpaceChar(c = this.read())) {
                result.appendCodePoint(c);
            }

            return result.toString();
        }

        public static boolean isSpaceChar(int c) {
            return c == 32 || c == 10 || c == 13 || c == 9 || c == -1;
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void printf(String format, Object... objects) {
            writer.printf(format, objects);
        }

        public void close() {
            writer.close();
        }

    }
}