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:
// package CodeForces;
//package ;
import java.io.*;
import java.util.*;

public class Problem_1088C
{
	static long oz(long x,int idx)
	{
		long rem=x%n;
		long t=n-rem;
		long inc=t+idx;
		return inc;
	}
	static int n;
//	static int mod
	static StringBuilder sb;
	public static void main(String[] args) throws IOException 
	{
		Scanner sc = new Scanner();
		PrintWriter pw = new PrintWriter(System.out);
		n=sc.nextInt();
		if(n==1)
		{
			System.out.println(0);
			return;
		}
		long[]a=new long[n];
		for(int i=0;i<n;i++)a[i]=sc.nextLong();
		int c=0;
		sb=new StringBuilder();
		if(a[n-1]<n)
		{
			long inc=n-a[n-1];
			for(int i=0;i<n;i++)
				a[i]+=inc;

			sb.append(1+" "+n+" "+inc+"\n");
			c++;
		}
		long total =0;
		for(int i=n-2;i>=0;i--)
		{
			a[i]+=total;
			long inc=oz(a[i],i+1);
			
			sb.append(1+" "+(i+1)+" "+inc+"\n");
			
			total+=inc;
			a[i]+=inc;
			c++;
		}
//		for(int i=0;i<n-1;i++)
//			a[i]%=n;
		sb.append(2+" "+(n-1)+" "+n);
		c++;
		System.out.println(c);
		System.out.println(sb.toString());
		pw.close();    
	}
	static class Scanner {
		BufferedReader br;
		StringTokenizer st;
		
		Scanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
		
		String next() throws IOException {
			while (st == null || !st.hasMoreTokens()) {
				st = new StringTokenizer(br.readLine());
			}
			return st.nextToken();
		}
		
		int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
		
		long nextLong() throws IOException {
			return Long.parseLong(next());
		}
		
		double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
		
		String nextLine() throws IOException {
			return br.readLine();
		}
		boolean hasnext() throws IOException{
			return br.ready();
		}
		
	}
}