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.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 27);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastReader in = new FastReader(inputStream);
            PrintWriter out = new PrintWriter(outputStream);
            AMultiplesOfLength solver = new AMultiplesOfLength();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class AMultiplesOfLength {
        public void solve(int testNumber, FastReader s, PrintWriter w) {
            int n = s.nextInt();
            long[] a = new long[n];
            for (int i = 0; i < n; i++) a[i] = s.nextInt();
            if (n == 1) {
                w.println("1 1");
                w.println(-a[0]);
                w.println("1 1");
                w.println(0);
                w.println("1 1");
                w.println(0);
                return;
            }
            w.println(1 + " " + (n - 1));
            for (int i = 0; i < n - 1; i++) {
                long x = (n - (a[i] % n)) % n;
                x *= func.modinv(n - 1, n);
                x %= n;
                w.print(x * (n - 1) + " ");
                a[i] += x * (n - 1);
            }
            w.println();
            w.println(1 + " " + n);
            for (int i = 0; i < n; i++) {
                long x = (a[i] / n) * n;
                w.print(-x + " ");
                a[i] -= x;
            }
            w.println();
            w.println(n + " " + n);
            w.println(-a[n - 1]);
        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private FastReader.SpaceCharFilter filter;

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

        public int read() {

            if (numChars == -1)
                throw new InputMismatchException();

            if (curChar >= numChars) {

                curChar = 0;

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

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

            return buf[curChar++];
        }

        public int nextInt() {

            int c = read();

            while (isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-') {
                sgn = -1;
                c = read();
            }

            int res = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();

                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));

            return res * sgn;
        }

        public boolean isSpaceChar(int c) {

            if (filter != null)
                return filter.isSpaceChar(c);

            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class func {
        public static long modinv(long a, long m) {
            long m0 = m, y = 0, x = 1, q, t;
            if (m == 1) return 0;
            while (a > 1) {
                q = a / m;
                t = m;
                m = a % m;
                a = t;
                t = y;
                y = x - q * y;
                x = t;
            }
            if (x < 0) x += m0;
            return x;
        }

    }
}