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.util.StringTokenizer;

public class A {
    private FastScanner in;
    private PrintWriter out;

    public A(FastScanner in, PrintWriter out) {
        this.in = in;
        this.out = out;
    }

    public static void main(String[] args) {
        try (
                FastScanner in = new FastScanner(System.in);
                PrintWriter out = new PrintWriter(System.out);
        ) {
            A solution = new A(in, out);
            solution.solve();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    public void solve() throws IOException {
        int n = in.nextInt();
        int[] array = new int[n];
        for (int i = 0; i < n; i++) {
            array[i] = in.nextInt();
        }
        //first
        out.println("1 1");
        out.print(-array[0]);
        out.println();
        //second
        out.println("1 " + n);
        out.print(0);
        for (int i = 1; i < n; i++) {
            out.write(' ');
            out.print((long) -array[i] * array.length);
        }
        out.println();
        //third
        if (n > 1) {
            out.println("2 " + n);
            for (int i = 1; i < n; i++) {
                out.print((array.length - 1L) * array[i]);
                out.write(' ');
            }
            out.println();
        } else {
            out.println("1 1");
            out.println(0);
        }
    }


    public static class FastScanner implements Closeable {
        BufferedReader bufferedReader;
        StringTokenizer stringTokenizer;

        public FastScanner(InputStream inputStream) {
            this.bufferedReader = new BufferedReader(new InputStreamReader(inputStream));
        }

        public FastScanner(File file) throws FileNotFoundException {
            this(new FileInputStream(file));
        }

        public String next() throws IOException {
            while (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
                String line = bufferedReader.readLine();
                if (line == null) {
                    throw new EOFException("End of input stream is reached.");
                }
                stringTokenizer = new StringTokenizer(line);
            }
            return stringTokenizer.nextToken();
        }

        public String nextLine() throws IOException {
            stringTokenizer = null;
            return bufferedReader.readLine();
        }

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

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

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

        @Override
        public void close() throws IOException {
            bufferedReader.close();
        }
    }
}