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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class TaskC {

    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));

        // Start writing your solution here. -------------------------------------

        /*
            int n      = sc.nextInt();        // read input as integer
            long k     = sc.nextLong();       // read input as long
            double d   = sc.nextDouble();     // read input as double
            String str = sc.next();           // read input as String
            String s   = sc.nextLine();       // read whole line as String

            int result = 3*n;
            out.println(result);                    // print via PrintWriter
        */

        // Stop writing your solution here. -------------------------------------



            long n = sc.nextLong();
            List<Long> st = new ArrayList<>((int)n) ;
            for (int i=0; i<n; i++) {
                st.add(i, sc.nextLong());
            }

            // eliminate first:
            long first = st.get(0);
            st.set(0, n - (first % n));
            out.println("1 1");
            out.println(-first % n);

            if (n == 1) {
                out.println("1 1");
                out.println(-first /n * n);
                out.println("1 1");
                out.println("0");
                out.close();

                return;
            }

            out.println("2 " + n);
            for (int i=1; i<n; i++) {
                long value = st.get(i);
                long Y = - value % n;
                out.print(-Y*(n-1));
                out.print(" ");
            }
            out.println();

            out.println("1 " + n);
            out.print(-first /n * n);
            out.print(" ");
            for (int i=1; i<n; i++) {
                long value = st.get(i);
                long X = value / n + value % n;
                out.print(-X*n);
                out.print(" ");
            }
            out.println();






        out.close();
    }



    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out;

    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

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

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

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

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

        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

    }
}