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.math.*;
     
    public class C
    {
        public static void process(int test_number)throws IOException
        {
            int n = ni();
            long arr[] = new long[n + 1];

            for(int i = 1; i <= n; i++)
                arr[i] = nl();

            if(n == 1){
                pn("1 1 \n" + (arr[1] * (-1l)));
                pn("1 1 \n0");
                pn("1 1 \n0");
                return ;
            }

            long len = n;
            pn("1 "+n);
            for(int i = 1; i <= n; i++){
                p((arr[i] * (-1l) * n)+" ");
            }
            p('\n');

            pn("1 "+(n - 1));
            for(int i = 1; i < n; i++){
                p(((n - 1) * (arr[i])) + " ");
            }
            p('\n');

            pn(n + " " + n);
            pn((arr[n] * n - arr[n]));
        }
         
        static final int oo = 1234567899;
        static final long mod = (long)1e9+7l;
        
        static FastReader sc;
        static PrintWriter out;
        public static void main(String[]args)throws IOException
        {
            out = new PrintWriter(System.out);
            sc = new FastReader();
     
            long s = System.currentTimeMillis();
            int t = 1;
            //t = ni();
            for(int i = 1; i <= t; i++)
                process(i);
     
            out.flush();
            System.err.println(System.currentTimeMillis()-s+"ms");
        }

        static void trace(Object... o){ System.err.println(Arrays.deepToString(o)); };
        static void pn(Object o){ out.println(o); }
        static void p(Object o){ out.print(o); }
        static int ni()throws IOException{ return Integer.parseInt(sc.next()); }
        static long nl()throws IOException{ return Long.parseLong(sc.next()); }
        static double nd()throws IOException{ return Double.parseDouble(sc.next()); }
        static String nln()throws IOException{ return sc.nextLine(); }
        static long gcd(long a, long b)throws IOException{ return (b==0)?a:gcd(b,a%b);}
        static int gcd(int a, int b)throws IOException{ return (b==0)?a:gcd(b,a%b); }
        static int bit(long n)throws IOException{ return (n==0)?0:(1+bit(n&(n-1))); }
        
        static class FastReader{ 
            BufferedReader br; 
            StringTokenizer st; 
      
            public FastReader(){ 
                br = new BufferedReader(new InputStreamReader(System.in)); 
            } 
      
            String next(){ 
                while (st == null || !st.hasMoreElements()){ 
                    try{ st = new StringTokenizer(br.readLine()); } catch (IOException  e){ e.printStackTrace(); } 
                } 
                return st.nextToken(); 
            } 
      
            String nextLine(){ 
                String str = ""; 
                try{ str = br.readLine(); } catch (IOException e) { e.printStackTrace(); } 
                return str; 
            } 
        } 
    }