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.*; 
//import javafx.util.*; 
import java.math.*;
//import java.lang.*;
public class Main 
{ 
  //   static long mod=1000000007;
     static HashSet<Integer> adj[];
     static boolean vis[];
  //   static int n[];
  //   static ArrayList<Integer> arr[];
  // //  static long ans=0;
  //   static boolean vis[][];
  //   static final long oo=(long)1e18;
    // static int par[];
    // static long child[];
    // static HashMap<String,Long> hm=new HashMap<>();
    static int ver=0;static int edge=0;
     public static void main(String[] args) throws IOException {  
        PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        br = new BufferedReader(new InputStreamReader(System.in));
      //  int test=nextInt();
        int test=1;
        outer: while(test--!=0){
            int n=nextInt();
            long arr[]=new long[n];
            for(int i=0;i<n;i++){
                arr[i]=nextLong();
            }
            if(n==1){
                pw.println("1 1");
                pw.println(-1*arr[0]);
                 pw.println("1 1");
                pw.println("0");
                 pw.println("1 1");
                pw.println("0");
                continue outer;
            }
            pw.println("1 "+(n-1));
            for(int i=0;i<n-1;i++){
                long a=arr[i]%n;
                arr[i]+=(a)*(n-1);
                pw.print((n-1)*a+" ");
            }
            pw.println();
            pw.println((n)+" "+(n));
            pw.println((-1*arr[n-1]));
            arr[n-1]=0;
            pw.println("1 "+(n));
            for(int i=0;i<n;i++){
                pw.print(-1*arr[i]+" ");
            }
            pw.println();

        }
           
        pw.close();
    }
    static void dfs(int i){
        vis[i]=true;
        ver++;
        for(int v:adj[i]){
            edge++;
            if(!vis[v]){
                dfs(v);
            }
        }
    }
    
    
    static class compare implements Comparable<compare>{
         String s;
         compare(String s){
            this.s=s;
        }
        public  int compareTo(compare t){
            return compareVersion(s,t.s);
        }
        public  int compareVersion(String version1, String version2) {
            String[] nums1 = version1.split("\\.");
            String[] nums2 = version2.split("\\.");
            int n1 = nums1.length, n2 = nums2.length;

            // compare versions
            int i1, i2;
            for (int i = 0; i < Math.max(n1, n2); ++i) {
              i1 = i < n1 ? Integer.parseInt(nums1[i]) : 0;
              i2 = i < n2 ? Integer.parseInt(nums2[i]) : 0;
              if (i1 != i2) {
                return i1 > i2 ? 1 : -1;
              }
            }
            // the versions are equal
            return 0;
        }
    }
  
    
    static class Pair{
        int a;int b;
        Pair(int a,int b){
          //  this.index=index;
            this.a=a;
            this.b=b;
            
            //this.z=z;
        }   
    }
   static void update(long tree[],int idx,long val){
        //println(idx);
        while(idx<1000006){
            
            tree[idx]+=val;
            idx+=(idx)&(-idx);
        }
    }   
    static long sum(long tree[],int idx){
        long sum=0;
        while(idx>0){
           
            sum+=tree[idx];
            idx-=(idx)&(-idx);
        }
        return sum;
    }
    public static BufferedReader br;
    public static StringTokenizer st;
    public static String next() {
        while (st == null || !st.hasMoreTokens()) {
       try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                throw new RuntimeException(e);
            }
        }
        return st.nextToken();
    }
 
    public static Integer nextInt() {
        return Integer.parseInt(next());
    }
    public static Long nextLong() {
        return Long.parseLong(next());
    }
 
    public static Double nextDouble() {
        return Double.parseDouble(next());
    }
    // static class Pair{
    //     int x;int y;
    //     Pair(int x,int y,int z){
    //         this.x=x;
    //         this.y=y;
    //        // this.z=z;
    //      //   this.z=z;
    //       //  this.i=i;
    //     }
    // }
    // static class sorting implements Comparator<Pair>{
    //     public int compare(Pair a,Pair b){
    //         //return (a.y)-(b.y);
    //         if(a.y==b.y){
    //             return -1*(a.z-b.z);
    //         }
    //         return (a.y-b.y);
    //     }
   // }

    static long ncr(long n,long r){
        
        if(r==0)
            return 1l;
        long val=ncr(n-1,r-1);
        val=(n*val);
        val=(val/r);
        return val;
    }

    public static int[] na(int n)throws IOException{
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = nextInt();
        return a;
    }
    static class query implements Comparable<query>{
        int l,r,idx,block;
        static int len;
        query(int l,int r,int i){
            this.l=l;
            this.r=r;
            this.idx=i;
            this.block=l/len;
        }   
        public int compareTo(query a){
            return block==a.block?r-a.r:block-a.block;
        }
    }
    
    // static class sorting implements Comparator<Pair>{  
    //     public int compare(Pair a1,Pair a2){  
    //         if(o1.a==o2.a)
    //             return (o1.b>o2.b)?1:-1;  
    //         else if(o1.a>o2.a)  
    //             return 1;  
    //         else  
    //             return -1;  
    //     }
    // }  
    static boolean isPrime(int n) { 
        if (n <= 1) 
            return false; 
        if (n <= 3) 
            return true; 
        if (n % 2 == 0 ||  
            n % 3 == 0) 
            return false; 
      
        for (int i = 5; 
                 i * i <= n; i = i + 6) 
            if (n % i == 0 || 
                n % (i + 2) == 0) 
                return false; 
      
        return true; 
    } 
    static int gcd(int a, int b) { 
      if (b == 0) 
        return a; 
      return gcd(b, a % b);  
    }  
    // To compute x^y under modulo m 
    static long power(long x, long y, long m){ 
        if (y == 0) 
            return 1;      
        long p = power(x, y / 2, m) % m; 
        p = (p * p) % m; 
      
        if (y % 2 == 0) 
            return p; 
        else
            return (x * p) % m; 
    }
    static long fast_pow(long base,long n,long M){
        if(n==0)
           return 1;
        if(n==1)
        return base;
        long halfn=fast_pow(base,n/2,M);
        if(n%2==0)
            return ( halfn * halfn ) % M;
        else
            return ( ( ( halfn * halfn ) % M ) * base ) % M;
    }
       static long modInverse(long n,long M){
        return fast_pow(n,M-2,M);
    }
    // (1,1)   

    //     (3,2)   (3,5)

}