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.util.*;
import java.io.*;

public class File {
    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            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());
        }
    }

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




		int n = sc.nextInt();
		long[] a = new long[n];
		
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextLong();
		}
		
		
		long N = (long)n;
		
		// Move 1:
			// For first N-1 elements, add some multiple of N-1
			// Such that result is multiple of N.
		if (n == 1) {
	        out.println(1 + " " + 1);
	        out.print(0);
		}
		else {
		    out.println(1 + " " + (n-1));
		    
		    for (int i = 0; i < n - 1; i++) {
    			long offset = (long)Math.abs(a[i]);
    			
    			if (a[i] < 0) {
    			    long add = -((N-1) * offset);
    				out.print(add + " ");
    				a[i] += add;
    			}
    			else {
    			    long add = ((N-1) * offset);
    				out.print(add + " ");
    				a[i] += add;
    			}
    		}
		}
		
		out.println();
		
		// Move 2:
			// For last element, subtract its value from itself.
		out.println(n + " " + n);
		out.println(-a[n-1]);
		a[n-1] = 0;
		
		// Move 3:
			// For all N elements, subtract multiple of N to become 0.
		out.println(1 + " " + n);
		for (int i = 0; i < n; i++) {
			out.print(-a[i] + " ");
			a[i] = 0;
		}
		
		
		
		
		
		

		
		
		out.close();
	}
}