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.math.BigInteger;
import java.util.*;

public class Main {

	static long sx = 0, sy = 0, mod = (long) (1e9 + 7);

	// static HashSet<Integer>[] a;
	static Double[][][] dp;
	static long[] fa;
	static long[] farr;
	public static PrintWriter out = new PrintWriter(System.out);
	static ArrayList<pair> pa = new ArrayList<>();
	static long[] fact = new long[(int) 1e6];
	static StringBuilder sb = new StringBuilder();
	static boolean cycle = false;
	static long m = 998244353;
	static long[] no, col;
	static String s;
	static long k = 0, n = 0, one = 0;
	static int cnt;
	// static long[] dp;
	static long[] p;
	static long[] ans;
	static int[][] a = new int[2][2];
	static int[][] b = new int[2][2];
	static Double[] x;
	static Double[] y;

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

		// Scanner scn = new Scanner(new BufferedReader(new
		// InputStreamReader(System.in)));

		Reader scn = new Reader();

		int t = 1;

		z: while (t-- != 0) {

			int n = scn.nextInt();

			long[] a = scn.nextLongArray(n);

			StringBuilder sb = new StringBuilder();

			if (n == 1) {

				System.out.println(1 + " " + 1);
				System.out.println(0);
				System.out.println(1 + " " + 1);
				System.out.println(0);
				System.out.println(1 + " " + 1);
				System.out.println(-a[0]);

				continue z;
			}

			sb.append(1 + " " + (n - 1));
			sb.append("\n");

			for (int i = 0; i < n - 1; i++) {

				long val = ((a[i] % n + n) % n) * (n - 1);
				a[i] += val;
				sb.append(val + " ");
			}

			sb.append("\n");
			sb.append(2 + " " + (n));
			sb.append("\n");

			for (int i = 1; i < n; i++) {
				long val = ((a[i] % n + n) % n) * (n - 1);
				sb.append(val + " ");
				a[i] += val;
			}
			sb.append("\n");

			sb.append(1 + " " + n);
			sb.append("\n");

			for (long i : a)
				sb.append(-i + " ");

			System.out.println(sb);

		}

	}

	// _________________________TEMPLATE_____________________________________________________________

	// public static long lcm(long x, long y) {
	//
	// return (x * y) / gcd(x, y);
	// }
	//
	// private static long gcd(long x, long y) {
	// if (x == 0)
	// return y;
	//
	// return gcd(y % x, x);
	// }
	//
	// static class comp implements Comparator<Integer> {
	//
	// @Override
	// public int compare(Integer p1, Integer p2) {
	//
	// return p2 - p1;
	//
	// }
	// }
	//
	// }
	//
	// public static long pow(long a, long b) {
	//
	// if (b < 0)
	// return 0;
	// if (b == 0 || b == 1)
	// return (long) Math.pow(a, b);
	//
	// if (b % 2 == 0) {
	//
	// long ret = pow(a, b / 2);
	// ret = (ret % mod * ret % mod) % mod;
	// return ret;
	// }
	//
	// else {
	// return ((pow(a, b - 1) % mod) * a % mod) % mod;
	// }
	// }

	private static class pair implements Comparable<pair> {

		int i, t;

		pair(int a, int b) {
			i = a;
			t = b;
		}

		@Override
		public int compareTo(pair o) {
			return o.t - this.t;
		}

		// @Override
		//
		// public int hashCode() {
		// return i;
		// }
		//
		// @Override
		//
		// public boolean equals(Object o) {
		//
		// pair p = (pair) o;
		// return this.i == p.i;
		// }

	}

	private static String reverse(String s) {

		return new StringBuilder(s).reverse().toString();
	}

	public 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[1000000 + 1]; // 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 int[] nextIntArray(int n) throws IOException {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextInt();
			}
			return arr;
		}

		public long[] nextLongArray(int n) throws IOException {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLong();
			}
			return arr;
		}

		public int[][] nextInt2DArray(int m, int n) throws IOException {
			int[][] arr = new int[m][n];
			for (int i = 0; i < m; i++) {
				for (int j = 0; j < n; j++)
					arr[i][j] = nextInt();
			}
			return arr;
		}

		public long[][] nextInt2DArrayL(int m, int n) throws IOException {
			long[][] arr = new long[m][n];
			for (int i = 0; i < m; i++) {
				for (int j = 0; j < n; j++)
					arr[i][j] = nextInt();
			}
			return arr;
		}
		// kickstart - Solution
		// atcoder - Main
	}

}