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.FileInputStream;
import java.io.FileOutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintStream;
import java.util.Locale;
import java.util.StringTokenizer;

public class Solution implements Runnable {
	
	private PrintStream out;
	private BufferedReader in;
	private StringTokenizer st;
	
	public void solve() throws IOException {
		long time0 = System.currentTimeMillis();
		
		int n = nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = nextInt();
		}
		AnswerLine[] answer = solve(n, a);
		for (int i = 0; i < 3; i++) {
			out.println(answer[i]);
		}
		
		System.err.println("time: " + (System.currentTimeMillis() - time0));
	}
	
	private AnswerLine[] solve(int n, int[] a) {
		AnswerLine[] result = new AnswerLine[3];
		result[0] = new AnswerLine(0, 0);
		result[0].b[0] = -a[0];
		a[0] = 0;
		if (n == 1) {
			result[1] = new AnswerLine(0, 0);
			result[2] = new AnswerLine(0, 0);
			return result;
		}
		result[1] = new AnswerLine(1, n - 1);
		result[2] = new AnswerLine(0, n - 1);
		for (int i = 1; i < n; i++) {
			result[1].b[i - 1] = 1L * (n - 1) * a[i];
		}
		for (int i = 0; i < n; i++) {
			result[2].b[i] = -1L * n * a[i];
		}
		return result;
	}
	
	private static final class AnswerLine {
		private int l;
		private int r;
		private long[] b;
		private AnswerLine(int l, int r) {
			this.l = l;
			this.r = r;
			this.b = new long[r - l + 1];
		}
		public String toString() {
			StringBuilder buf = new StringBuilder();
			buf.append((l + 1) + " " + (r + 1)).append("\n");
			for (int i = 0; i < b.length; i++) {
				if (i > 0) {
					buf.append(' ');
				}
				buf.append(b[i]);
			}
			return buf.toString();
		}
	}

	public double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}
	
	public long nextLong() throws IOException {
		return Long.parseLong(next());
	}
	
	public int nextInt() throws IOException {
		return Integer.parseInt(next());
	}
	
	public String next() throws IOException {
		while (!st.hasMoreTokens()) {
			String line = in.readLine();
			if (line == null) {
				return null;
			}
			st = new StringTokenizer(line);
		}
		return st.nextToken();
	}
	
	@Override
	public void run() {
		try {
			solve();
			out.close();
		} catch (Throwable e) {
			throw new RuntimeException(e);
		}
	}
	
	public Solution(String name) throws IOException {
		Locale.setDefault(Locale.US);
		if (name == null) {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintStream(new BufferedOutputStream(System.out));
		} else {
			in = new BufferedReader(new InputStreamReader(new FileInputStream(name + ".in")));
			out = new PrintStream(new BufferedOutputStream(new FileOutputStream(name + ".out")));
		}
		st = new StringTokenizer("");
	}
	
	public static void main(String[] args) throws IOException {
		new Thread(new Solution(null)).start();
	}
}