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.*;

public class Main {
	
	public static void main(String[] args) throws IOException {
		FastIO in = new FastIO(System.in);
		
		int n = in.nextInt();
		long[] a = new long[n];
		
		for (int i = 0; i < n; i++) a[i] = in.nextLong();
		
		if (n == 1) {
			System.out.println("1 1");
			System.out.println(-a[0]);
			System.out.println("1 1");
			System.out.println("0");
			System.out.println("1 1");
			System.out.println("0");
		} else {
			System.out.println("1 1");
			System.out.println(-a[0]);
			a[0]=0;
			System.out.println("2 "+ (n));
			for(int i = 1; i < n; i++)
			{
				System.out.print(a[i]*(n-1)+" ");
				a[i] = a[i] * n;
			}
			System.out.println();
			System.out.println("1 " + n);
			for(int i = 0; i < n; i++) System.out.print(-a[i]+" ");
		}
		
		in.close();
	}
	
	public static class FastIO {
		private InputStream dis;
		private byte[] buffer = new byte[1 << 17];
		private int pointer = 0;
	
		public FastIO(String fileName) throws IOException {
			dis = new FileInputStream(fileName);
		}
	
		public FastIO(InputStream is) throws IOException {
			dis = is;
		}
	
		public int nextInt() throws IOException {
			int ret = 0;
			byte b;
			
			do {
				b = nextByte();
			} while (b <= ' ');
			
			boolean negative = false;
			if (b == '-') {
				negative = true;
				b = nextByte();
			}
			
			while (b >= '0' && b <= '9') {
				ret = 10 * ret + b - '0';
				b = nextByte();
			}
	
			return (negative) ? -ret : ret;
		}
	
		public long nextLong() throws IOException {
			long ret = 0;
			byte b;
			
			do {
				b = nextByte();
			} while (b <= ' ');
			
			boolean negative = false;
			if (b == '-') {
				negative = true;
				b = nextByte();
			}
			
			while (b >= '0' && b <= '9') {
				ret = 10 * ret + b - '0';
				b = nextByte();
			}
			
			return (negative) ? -ret : ret;
		}
	
		public byte nextByte() throws IOException {
			if (pointer == buffer.length) {
				dis.read(buffer, 0, buffer.length);
				pointer = 0;
			}
			return buffer[pointer++];
		}
	
		public String next() throws IOException {
			StringBuffer ret = new StringBuffer();
			byte b;
			
			do {
				b = nextByte();
			} while (b <= ' ');
			
			while (b > ' ') {
				ret.appendCodePoint(b);
				b = nextByte();
			}
	
			return ret.toString();
		}
	
		public void close() throws IOException {
			dis.close();
		}
	}
}