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.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

public class Round659 {

	static int rec = 0;
	static int X[] = { -1, 0, 0, 1 };
	static int Y[] = { 0, -1, 1, 0 };
	static long mod = 1000000007;

	static class Reader {
		final private int BUFFER_SIZE = 1 << 16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer, bytesRead;

		public Reader() {
			din = new DataInputStream(System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public Reader(String file_name) throws IOException {
			din = new DataInputStream(new FileInputStream(file_name));
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public String readLine() throws IOException {
			byte[] buf = new byte[64]; // line length
			int cnt = 0, c;
			while ((c = read()) != -1) {
				if (c == '\n')
					break;
				buf[cnt++] = (byte) c;
			}
			return new String(buf, 0, cnt);
		}

		public int nextInt() throws IOException {
			int ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (neg)
				return -ret;
			return ret;
		}

		public long nextLong() throws IOException {
			long ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}

		public double nextDouble() throws IOException {
			double ret = 0, div = 1;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();

			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (c == '.') {
				while ((c = read()) >= '0' && c <= '9') {
					ret += (c - '0') / (div *= 10);
				}
			}

			if (neg)
				return -ret;
			return ret;
		}

		private void fillBuffer() throws IOException {
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1)
				buffer[0] = -1;
		}

		private byte read() throws IOException {
			if (bufferPointer == bytesRead)
				fillBuffer();
			return buffer[bufferPointer++];
		}

		public void close() throws IOException {
			if (din == null)
				return;
			din.close();
		}
	}

	public static long[] initArray(int n, Reader scan) throws IOException {

		long arr[] = new long[n];
		for (int i = 0; i < n; i++) {
			arr[i] = scan.nextLong();
		}

		return arr;
	}

	public static long sum(long arr[]) {

		long sum = 0;
		for (long i : arr) {
			sum += (long) i;
		}

		return sum;
	}

	public static long max(long arr[]) {

		long max = Long.MIN_VALUE;

		for (long i : arr) {
			max = Math.max(i, max);
		}

		return max;
	}

	public static long min(long arr[]) {
		long min = Long.MAX_VALUE;

		for (long i : arr) {
			min = Math.min(i, min);
		}

		return min;
	}

	public static List<Integer>[] initAdjacency(int n, int e, Reader scan, boolean type) throws IOException {

		List<Integer> adj[] = new ArrayList[n + 1];

		for (int i = 0; i < e; i++) {
			int u = scan.nextInt();
			int v = scan.nextInt();

			if (adj[u] == null)
				adj[u] = new ArrayList<>();
			if (type && adj[v] == null)
				adj[v] = new ArrayList<>();

			adj[u].add(v);

			if (type)
				adj[v].add(u);

		}

		return adj;
	}

	public static void main(String[] args) throws IOException {

		Reader scan = new Reader();
//		Scanner scan = new Scanner(System.in);

		int t = 1;
		while (t-- > 0) {

			int n = scan.nextInt();
			
			long arr[]=initArray(n, scan);
			C(n, arr);
		}

	}
	
	public static void C(int n, long arr[]) {
		
		
		if(n==1) {
			
			System.out.println("1 1");
			System.out.println(-arr[0]);
			System.out.println("1 1");
			System.out.println(0);
			System.out.println("1 1");
			System.out.println(0);
			return;
			
		}
		
		
		System.out.println(1+" "+(n-1));
		
		for(int i=0;i<n-1;i++) {
			
			System.out.print((arr[i]*(n-1))+" ");
		}
		
		System.out.println();

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

		System.out.println(1+" "+(n));
		for(int i=0;i<n;i++) {
			
			if(i==n-1) {
				System.out.print(0+" ");
			}else {
				System.out.print(-(arr[i]*n)+" ");
			}
		}
		
		System.out.println();
		
		
	}
	
	public static void B(int n, long arr[]) {
		
		Arrays.sort(arr);
		
		
		
		double upperVal= Math.pow(10, 12/(n-1));
		
		
		long ans=Long.MAX_VALUE;
		
		for(long i=1;i<=(long)Math.ceil(upperVal);i++) {
			
			long curAns=0;
			
			for(int j=0;j<n;j++) {
				
				curAns+= (long)Math.abs(Math.pow(i, j)- arr[j]);
				
			}
			
			ans=Math.min(ans, curAns);
			
		}
		
		System.out.println(ans);
		return;
		
//		
//		if(n<=32) {
//			
//			
//			
//			
//			
//			
//			
//		}else {
//			
//			
//			long ans=0;
//			
//			for(long val: arr) {
//				
//				ans+= Math.abs(val-1);
//			}
//			
//			System.out.println(ans);
//			
//		}
		
	}
	
	public static void A(int n,String arr[]) {
		
		int count[]=new int[26];
		
		for(String s: arr) {
			for(int i=0;i<s.length();i++) {
				count[s.charAt(i)-'a']++;
			}
		}
		
		
		for(Integer x: count) {
			if(x%n!=0) {
				System.out.println("NO");
				return;
			}
			
		}
		
		System.out.println("YES");
		
	}

	
	
	

}

class MyPair {

	int value;
	int weight;

	public MyPair(int value, int w) {
		this.value = value;
		weight = w;
	}

}