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.util.*;
import java.io.*;

public class Main{



   public static long primeFactors(long n) 
{ 
    
    // Print the number of 2s that divide n 
  
    while (n%2 == 0) 
    { 
        return 2;
      
    } 
  
    // n must be odd at this point.  So we can skip  
    // one element (Note i = i +2) 
    for (long i = 3; i <= Math.sqrt(n); i = i+2) 
    { 
        // While i divides n, print i and divide n 
        while (n%i == 0) 
        { 
            return i;
            
             
        } 
    } 
  
    // This condition is to handle the case when n  
    // is a prime number greater than 2 
    if (n > 2) 
        return n;

    return 0;
       
} 

    

    public static boolean isPrime(long n) 
    { 
        // Corner cases 
        if (n <= 1) return false; 
        if (n <= 3) return true; 
      
        // This is checked so that we can skip  
        // middle five numbers in below loop 
        if (n % 2 == 0 || n % 3 == 0) return false; 
      
        for (long i = 5; i * i <= n; i = i + 6) 
            if (n % i == 0 || n % (i + 2) == 0) 
            return false; 
      
        return true; 
    } 

    public static void main(String[] args) {

        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader inp = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solver solver = new Solver();
        solver.solve(inp, out);
        out.close();
        
          }




    static class Solver {
        private void solve(InputReader inp, PrintWriter out1) {
            int n=inp.nextInt();
            int arr[] = new int[n];
            ArrayList<int[]> al = new ArrayList();
            for(int i=0;i<n;i++)
            {
                arr[i]=inp.nextInt();
            }
            if(arr[n-1]<n)
            {
                int ar[] = new int[3];
                ar[0]=1;
                ar[1]=n-1;
                ar[2]=n-arr[n-1]-1;
                al.add(ar);
                for(int k=0;k<=ar[1];k++)
                {
                    arr[k]+=ar[2];
                }
            }
            int num=  arr[n-1]+1;
            int rem=arr[n-1]-1;
            for(int i=n-2;i>=0;i--)
            {
                int x = num-(arr[i]%num)+rem;
                x%=num;
                if(x==0)
                {
                    rem--;
                    continue;
                    
                }    
                rem--;
                int ar[] = new int[3];
                ar[0]=1;
                ar[1]=i;
                ar[2]=x;
                al.add(ar);
                for(int k=0;k<=ar[1];k++)
                {
                    arr[k]+=ar[2];
                }
            }
            int ar[] = new int[3];
            ar[0]=2;
            ar[1]=n-1;
            ar[2]=num;
            al.add(ar);

            out1.println(al.size());

            for(int i=0;i<al.size();i++)
            {
                int ar1[] = al.get(i);
                out1.println(ar1[0]+" "+(ar1[1]+1)+" "+ar1[2]);
                
                
            }
    }



    
}






    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;

        InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

        public long nextLong() {
            return Long.parseLong(next());
        }
    }
}
class ele{
    long value;
    long i;
    boolean flag;
    public ele(long value,long i)
    {
        this.value = value;
        this.i=i;
        this.flag = false;
    }
}