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 Exception {
		int t = 1;
		while (t-- > 0) {
			int n = ni();
			long a[] = nla(n);
			if (n == 1) {
				ps(1, 1);
				pln();
				pln(-a[0]);
				ps(1, 1);
				pln();
				pln(0);
				ps(1, 1);
				pln();
				pln(0);
				continue;
			}

			ps(1, n);
			pln();
			for (int i = 0; i < n; i++) {
				ps(-n * a[i]);
			}
			pln();
			ps(1, n - 1);
			pln();
			for (int i = 0; i < n - 1; i++) {
				ps((n - 1) * a[i]);
			}
			pln();
			ps(2, n);
			pln();
			for (int i = 1; i < n - 1; i++)
				ps("0");
			ps((n - 1) * a[n - 1]);
			pln();
		}
		flush();
	}

	static Reader in = new Reader();
	static StringBuilder output = new StringBuilder();
	static final int imod = 1000_000_007;
	static final long mod = 1000_000_007;
	static final int imax = 1000_000_000;
	static final int imin = -1000_000_000;
	static final long lmax = 1000_000_000_000_000_000L;
	static final long lmin = -1000_000_000_000_000_000L;

	//input functions
	static int ni() {return Integer.parseInt(in.next());}
	static long nl() {return Long.parseLong(in.next());}
	static String ns() {return in.next();}
	static double nd() {return Double.parseDouble(in.next());}
	static int[] eia(int n) {int a[] = new int[n]; return a;}
	static long[] ela(int n) {long a[] = new long[n]; return a;}
	static double[] eda(int n) {double a[] = new double[n]; return a;}
	static String[] esa(int n) {String a[] = new String[n]; return a;}
	static int[] nia(int n) {int a[] = new int[n]; for (int i = 0; i < n; i++)a[i] = ni(); return a;}
	static long[] nla(int n) {long a[] = new long[n]; for (int i = 0; i < n; i++)a[i] = nl(); return a;}
	static String[] nsa(int n) {String a[] = new String[n]; for (int i = 0; i < n; i++)a[i] = ns(); return a;}
	static double[] nda(int n) {double a[] = new double[n]; for (int i = 0; i < n; i++)a[i] = nd(); return a;}

	//output functions
	static void print(String a[]) {for (String i : a) System.out.print(i + " "); System.out.println();}
	static void print(int a[]) {for (int i : a) System.out.print(i + " "); System.out.println();}
	static void print(long a[]) {for (long i : a) System.out.print(i + " "); System.out.println();}
	static void print(double a[]) {for (double i : a) System.out.print(i + " "); System.out.println();}
	static void print(Object... a) {for (Object i : a) {System.out.print(i); System.out.print(" ");} System.out.println();}
	static void println(Object... a) {for (Object i : a) {System.out.print(i); System.out.print("\n");}}
	static void println() {System.out.println();}
	static void flush() {System.out.print(output); output = new StringBuilder();}
	static void pln(int []a) {for (int i : a) {output.append(i).append('\n');}}
	static void pln(long []a) {for (long i : a) {output.append(i).append('\n');}}
	static void pln(double []a) {for (double i : a) {output.append(i).append('\n');}}
	static void pln(String []a) {for (String i : a) {output.append(i).append('\n');}}
	static void pln(Object...a) {for (Object i : a) {output.append(i).append('\n');}}
	static void pln() {output.append('\n');}
	static void p(int []a) {for (int i : a) {output.append(i);}}
	static void p(long []a) {for (long i : a) {output.append(i);}}
	static void p(double []a) {for (double i : a) {output.append(i);}}
	static void p(String []a) {for (String i : a) {output.append(i);}}
	static void p(Object[] a) {for (Object i : a) {output.append(i);}}
	static void ps() {output.append(" ");}
	static void ps(int []a) {for (int i : a) {output.append(i).append(" ");}}
	static void ps(long []a) {for (long i : a) {output.append(i).append(" ");}}
	static void ps(double []a) {for (double i : a) {output.append(i).append(" ");}}
	static void ps(String []a) {for (String i : a) {output.append(i).append(" ");}}
	static void ps(Object... a) {for (Object i : a) {output.append(i).append(" ");}}



	//Utility functions
	static int lowerbound(int[]a, int key) { // returns index of smallest element larger than equal to given element between indices l and r inclusive
		int low = 0, high = a.length - 1, mid = (low + high) / 2; while (low < high) {if (a[mid] >= key)high = mid; else low = mid + 1; mid = (low + high) / 2;} return mid;
	}
	static int upperbound(int[]a, int key) {int low = 0, high = a.length - 1, mid = (low + high + 1) / 2; while (low < high) {if (a[mid] <= key) low = mid; else high = mid - 1; mid = (low + high + 1) / 2;} return mid;}
	static int lowerbound(int[]a, int l, int r, int key) { int low = l, high = r, mid = (low + high) / 2; while (low < high) { if (a[mid] >= key) high = mid; else low = mid + 1; mid = (low + high) / 2;} return mid;}
	static int upperbound(int[]a, int l, int r, int key) { // returns index of largest element smaller than equal to given element
		int low = l, high = r, mid = (low + high + 1) / 2; while (low < high) { if (a[mid] <= key) low = mid; else high = mid - 1; mid = (low + high + 1) / 2;} return mid;
	}

	static long powm(long a, long b, long mod) {long an = 1; long c = a % mod; while (b > 0) {if (b % 2 == 1)an = (an * c) % mod; c = (c * c) % mod; b >>= 1;} return an;}
	static long powm(long a, long b) {long an = 1; long c = a % mod; while (b > 0) {if (b % 2 == 1)an = (an * c) % mod; c = (c * c) % mod; b >>= 1;} return an;}
	static long pow(long a, long b) {long an = 1; long c = a; while (b > 0) {if (b % 2 == 1)an *= c; c *= c; b >>= 1;} return an;}
	static void reverse(int[]a) {for (int i = 0; i < a.length / 2; i++) {a[i] ^= a[a.length - i - 1]; a[a.length - i - 1] ^= a[i]; a[i] ^= a[a.length - i - 1];}}
	static void exit() {System.exit(0);}
	static int min(int... a) {int min = a[0]; for (int i : a)min = Math.min(min, i); return min;}
	static long min(long... a) {long min = a[0]; for (long i : a)min = Math.min(min, i); return min;}
	static double min(double... a) {double min = a[0]; for (double i : a)min = Math.min(min, i); return min;}
	static double max(double... a) {double max = a[0]; for (double i : a)max = Math.max(max, i); return max;}
	static int max(int... a) {int max = a[0]; for (int i : a)max = Math.max(max, i); return max;}
	static long max(long... a) {long max = a[0]; for (long i : a)max = Math.max(max, i); return max;}
	static long gcd(long... a) {long gcd = a[0]; for (long i : a)gcd = gcd(gcd, i); return gcd;}
	static int gcd(int... a) {int gcd = a[0]; for (int i : a)gcd = gcd(gcd, i); return gcd;}
	static int gcd(int a, int b) {if (b == 0)return a; if (a == 0) return b; return gcd(b, a % b);}
	static long gcd(long a, long b) {if (b == 0)return a; if (a == 0) return b; return gcd(b, a % b);}

	static class Pair {
		long la, lb;
		int a, b;
		double da, db;
		Pair() {} Pair(int c, int d) {a = c; b = d;}
		Pair(long c, long d) {la = c; lb = d;}
		Pair(int c, long d) { a = c; lb = d; }
		Pair(long c, int d) { la = c; b = d; }
		Pair(int c, double d) { a = c; db = d; }
		Pair(double c, double d) { da = c; db = d; }
		Pair(double c, int d) { da = c; b = d; }

		@Override
		public int hashCode() { return (a + " " + b).hashCode(); }
		public boolean equals(Object c) { return (a == (((Pair)c).a) && b == (((Pair)c).b)); }
	}

	static class Reader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;
		public Reader() {
			reader = new BufferedReader(new InputStreamReader(System.in));
			tokenizer = null;
		}
		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}
	}
}
class AL<T> extends java.util.ArrayList<T> {}
class HM<T, L> extends java.util.HashMap<T, L> {}
class HS<T> extends java.util.HashSet<T> {}