Problem: You're given an array a of length n. You can perform the following operations on it:

  * choose an index i (1 ≤ i ≤ n), an integer x (0 ≤ x ≤ 10^6), and replace a_j with a_j+x for all (1 ≤ j ≤ i), which means add x to all the elements in the prefix ending at i. 
  * choose an index i (1 ≤ i ≤ n), an integer x (1 ≤ x ≤ 10^6), and replace a_j with a_j \% x for all (1 ≤ j ≤ i), which means replace every element in the prefix ending at i with the remainder after dividing it by x. 



Can you make the array strictly increasing in no more than n+1 operations?

Input

The first line contains an integer n (1 ≤ n ≤ 2000), the number of elements in the array a.

The second line contains n space-separated integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^5), the elements of the array a.

Output

On the first line, print the number of operations you wish to perform. On the next lines, you should print the operations.

To print an adding operation, use the format "1 i x"; to print a modding operation, use the format "2 i x". If i or x don't satisfy the limitations above, or you use more than n+1 operations, you'll get wrong answer verdict.

Examples

Input

3
1 2 3


Output

0

Input

3
7 6 3


Output

2
1 1 1
2 2 4

Note

In the first sample, the array is already increasing so we don't need any operations.

In the second sample:

In the first step: the array becomes [8,6,3].

In the second step: the array becomes [0,2,3].

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.lang.*;
import java.math.*;
public class Main extends Thread  {
    boolean[] prime;
    FastScanner sc;
    PrintWriter pw;
    long startTime = System.currentTimeMillis();
    final class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            try {
                br = new BufferedReader(new InputStreamReader(System.in));
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                e.printStackTrace();
            }
        }

        public long nlo() {
            return Long.parseLong(next());
        }

        public String next() {
            if (st.hasMoreTokens()) return st.nextToken();
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                e.printStackTrace();
            }
            return st.nextToken();
        }

        public int ni() {
            return Integer.parseInt(next());
        }

        public String nli() {
            String line = "";
            if (st.hasMoreTokens()) line = st.nextToken();
            else try {
                return br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            while (st.hasMoreTokens()) line += " " + st.nextToken();
            return line;
        }

        public double nd() {
            return Double.parseDouble(next());
        }
    }
    public Main(ThreadGroup t,Runnable r,String s,long d )
    {
        super(t,r,s,d);
    }
    public void run()
    {
        sc=new FastScanner();
        pw=new PrintWriter(System.out);
        solve();
        pw.flush();
        pw.close();
    }
    public static void main(String[] args)
    {
        new Main(null,null,"",1<<25).start();
    }


    /////////////------------------------------------//////////////
    ////////////------------------Main-Logic--------//////////////
    ///////////-------------------------------------//////////////
   public static int[] visit,col;
   public static ArrayList<Integer>[] adj;
   public static long mod,c1,c2;
    public void solve() {
     int t=1;
     while(t-->0)
     {
       int n=sc.ni();
       long[] arr=new long[n+1];
       long m=100001L;
       long tmp=0;
       pw.println(n+1);
       for(int i=1;i<=n;i++)
       arr[i]=sc.ni();
       for(int i=n;i>0;i--)
       {
           arr[i]+=(tmp);
           long p=i;
           long y=p-arr[i];
           while(y<0L)
           y+=m;
           y%=m;
           pw.println("1 "+i+" "+y);
           tmp+=y;
       }
       pw.println("2 "+n+" "+m);
     }
   }
}