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.*;
import java.util.Map.Entry;


public class Main{

	static int inf=Integer.MAX_VALUE;
	static int mod=(int)1e9+7;
	static long [] fact;
	
	
	//divide into cases, brute force
	//sort, greedy, binary search
	//transform into graph
	
	static void solve(Reader in, Writer out){
		
		int n=in.ni();
		long a[]=in.rla(n);

		if(n==1){
			out.println("1 1\n"+-a[0]);
			a[0]=0;
			out.println("1 1\n"+-a[0]);
			out.println("1 1\n"+-a[0]);
			return;
		}

		out.println("1 "+(n-1));
		for(int i=0; i<n-1; ++i){
			long m=a[i]%n;
			a[i]+=m*(n-1);
			out.print(m*(n-1)+" ");
		}
		out.println();

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

	}

	public static void main(String[] args) throws IOException {
		Writer out=new Writer(System.out);
		Reader in=new Reader(System.in);	
		// mod=998244353;
		int ts=1;
		// ts=in.ni();
		while(ts-->0) {
			solve(in, out);
		}
		out.close();
	}
	static long ppow(long n, long m){
		if(m==0) return 1;
		long tmp=ppow(n,m/2);
		tmp=tmp*tmp%mod;
		return m%2==0 ? tmp : tmp*n %mod;
	}
	static long gcd(long n, long m){ return m==0 ? n : gcd(m, n%m); }
	static long lcm(long n, long m){ return n/gcd(n,m)*m; }
	static long nCr(int n, int r){ return fact[n]*ppow(fact[n-r], mod-2) % mod * ppow(fact[r],mod-2) % mod; }
	static void factInit(int n){ fact=new long[n]; fact[0]=1; for(int i=1; i<n; ++i) fact[i]=fact[i-1]*i % mod; }
	static int smaller(long [] a, long k){
		if(a[0]>k) return 0; int t=0;
		for(int j=a.length; j>=1; j/=2){ while(t+j<a.length && a[t+j]<k) t+=j; } return t+1;
	}
	static void reverse(int a[]){
		ArrayList<Integer> al=new ArrayList<>();
		for(int i: a) al.add(i); Collections.reverse(al);
		for(int i=0; i<al.size(); ++i) a[i]=al.get(i); 
	}
	static void reverse(long a[]){
		ArrayList<Long> al=new ArrayList<>();
		for(long i: a) al.add(i); Collections.reverse(al);
		for(int i=0; i<al.size(); ++i) a[i]=al.get(i); 
	}
	static void sort(int a[]) {
		ArrayList<Integer> al=new ArrayList<>();
		for(int i: a) al.add(i); Collections.sort(al);
		for(int i=0; i<a.length; ++i) a[i]=al.get(i);
	}
	static void sort(long a[]){
		ArrayList<Long> al=new ArrayList<>();
		for(long i: a) al.add(i); Collections.sort(al);
		for(int i=0; i<a.length; ++i) a[i]=al.get(i);
	}
	static void sort(pair [] p){
		ArrayList<pair> pl=new ArrayList<>(); for(pair pa: p) pl.add(pa);
		Collections.sort(pl, (p1, p2)->{
			return Long.compare(p1.u, p2.u)==0 ? Long.compare(p1.v,p2.v): Long.compare(p1.u,p2.u);
		});
		for(int i=0; i<p.length; ++i) p[i]=pl.get(i);
	}
	static void reverse(pair[] p){
		int n=p.length;
		for(int i=0; i<p.length/2; ++i){
			pair tmp=new pair(0,0); tmp.copy(p[i]);
			p[i].copy(p[n-1-i]); p[n-1-i].copy(tmp);
		}
	}
	static class pair{
		long u,v; pair(long g, long h){u=g; v=h;}
		void copy(pair p){u=p.u; v=p.v;};
	}
	static class Reader{	
		BufferedReader br;
		StringTokenizer to;
		Reader(InputStream stream){
			br=new BufferedReader(new InputStreamReader(stream));
			to=new StringTokenizer("");
		}
		String nextLine() {
			String line="";
			try { line=br.readLine(); }catch(IOException e) {};
			return line;
		}
		String ns() {
			while(!to.hasMoreTokens()) { try { to=new StringTokenizer(br.readLine()); }catch(IOException e) {} }
			return to.nextToken();
		}
		int ni() { return Integer.parseInt(ns()); }
		long nl() { return Long.parseLong(ns()); }
		int [] ra(int n) { int a[]=new int[n]; for(int i=0; i<n; i++) a[i]=ni(); return a; }
		long [] rla(int n) { long [] a =new long[n]; for(int i=0; i<n; ++i) a[i]=nl(); return a; }
	}	
	static class Writer extends PrintWriter{
		Writer(OutputStream stream){ super(stream); }
		void println(pair p){ println(p.u+" "+p.v); }
		void println(int a[]){ for(int i: a) print(i+" "); println(); }
	}
}