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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskA {
        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            int n = in.nextInt();
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = in.nextInt();
            }

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

            long[] d = egcd(n, n - 1);
            if (d[2] != 1) {
                throw new AssertionError();
            }
            // d[0] * n + d[1] * (n - 1) = 1
            out.println(1 + " " + n);
            for (int i = 0; i < n; i++) {
                if (i > 0) {
                    out.print(" ");
                }
                out.print(d[0] * n * (-a[i]));
            }
            out.println();
            out.println(1 + " " + (n - 1));
            for (int i = 0; i < n - 1; i++) {
                if (i > 0) {
                    out.print(" ");
                }
                out.print(d[1] * (n - 1) * (-a[i]));
            }
            out.println();
            out.println(2 + " " + n);
            for (int i = 1; i < n; i++) {
                if (i + 1 < n) {
                    out.print("0 ");
                } else {
                    out.println(d[1] * (n - 1) * (-a[i]));
                }
            }
        }

        private long[] egcd(long a, long b) {
            long[] d = new long[3];
            if (b == 0) {
                d[0] = 1;
                d[1] = 0;
                d[2] = a;
            } else {
                long[] nd = egcd(b, a % b);
                d[0] = nd[1];
                d[1] = nd[0] - (a / b) * nd[1];
                d[2] = nd[2];
            }
            return d;
        }

    }

    static class FastScanner {
        private BufferedReader in;
        private StringTokenizer st;

        public FastScanner(InputStream stream) {
            in = new BufferedReader(new InputStreamReader(stream));
        }

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

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

    }
}