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 R666A{

	public static void main(String[] args){
		JS scan = new JS();
		PrintWriter out = new PrintWriter(System.out);
		int n = scan.nextInt();
		long[] arr = new long[n];
		for(int i = 0; i < n; i++) arr[i] = scan.nextInt();

		if(n == 1){
			out.println("1 1");
			out.println("0");
			out.println("1 1");
			out.println("0");
			out.println("1 1");
			out.println(-arr[0]);
			out.flush();
			return;
		}

		out.println("1 1");
		out.println(n-arr[0]);
		arr[0] = arr[0]+(n-arr[0]);

		out.println("2 "+n);
		long minv = modInv(n-1, n);
		for(int i = 1; i < n; i++){
			if(i > 1) out.print(" ");
			long v = (-arr[i]*minv)%n*(n-1);
			out.print(v);
			arr[i] = arr[i]+v;
		}
		out.println();

		out.println("1 "+n);
		for(int i = 0; i < n; i++){
			if(i > 0) out.print(" ");
			out.print(-arr[i]);
		}
		out.println();
		out.flush();
	}

	static long modInv(long x, long mod) {
		if(x == 1) return 1;
		long r = mod % x;
		return modInv(r, x % r, 0, 1, mod / x, x / r);
	}

	static long modInv(long a, long b, long y0, long y1, long q0, long q1) {
		long y2 = y0 - y1*q0;
		return b == 0 ? y2 : modInv(b, a % b, y1, y2, q1, a / b);
	}	

	static class JS {
		public int BS = 1<<16;
		public char NC = (char)0;
		byte[] buf = new byte[BS];
		int bId = 0, size = 0;
		char c = NC;
		double num = 1;
		BufferedInputStream in;
	
		public JS() {
			in = new BufferedInputStream(System.in, BS);
		}
	
		public JS(String s) throws FileNotFoundException {
			in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
		}
	
		public char nextChar(){
			while(bId==size) {
				try {
					size = in.read(buf);
				}catch(Exception e) {
					return NC;
				}
				if(size==-1)return NC;
				bId=0;
			}
			return (char)buf[bId++];
		}
	
		public int nextInt() {
			return (int)nextLong();
		}
	
		public long nextLong() {
			num=1;
			boolean neg = false;
			if(c==NC)c=nextChar();
			for(;(c<'0' || c>'9'); c = nextChar()) {
				if(c=='-')neg=true;
			}
			long res = 0;
			for(; c>='0' && c <='9'; c=nextChar()) {
				res = (res<<3)+(res<<1)+c-'0';
				num*=10;
			}
			return neg?-res:res;
		}
	
		public double nextDouble() {
			double cur = nextLong();
			return c!='.' ? cur:cur+(cur < 0 ? -1*nextLong()/num : nextLong()/num);
		}
	
		public String next() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c>32) {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}
	}	
}