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 javax.print.attribute.standard.MediaSize;
import java.awt.*;
import java.nio.file.attribute.UserDefinedFileAttributeView;
import java.util.*;
import java.io.*;

public class Did_I_Deserve_It {

    /*

        Tyger! Tyger! burning bright
        In the forests of the night,
        What immortal hand or eye
        Could frame thy fearful symmetry?

        In what distant deeps or skies

        Burnt the fire of thine eyes?
        On what wings dare he aspire?
        What the hand, dare sieze the fire?

        And what shoulder, & what art,
        Could twist the sinews of thy heart?
        And when thy heart began to beat,
        What dread hand? & what dread feet?

        What the hammer? what the chain?
        In what furnace was thy brain?
        What the anvil? what dread grasp
        Dare its deadly terrors clasp?

        When the stars threw down their spears,
        And water’d heaven with their tears,
        Did he smile his work to see?
        Did he who made the Lamb make thee?

        Tyger! Tyger! burning bright
        In the forests of the night,
        What immortal hand or eye
        Dare frame thy fearful symmetry?

    */


    public static void main(String[] args) throws IOException {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);

        int n = Integer.parseInt(br.readLine());

        int arr[] = new int [n];

        StringTokenizer st1 = new StringTokenizer(br.readLine());

        for(int i = 0 ; i < n ; i++)
        {
            arr[i] = Integer.parseInt(st1.nextToken());
        }

        long cnt = 0;

        StringBuilder sb = new StringBuilder();

        for(int i = n - 1 ; i >= 0 ; i--)
        {
            arr[i] += cnt;

            int tmp = (n + i) - arr[i];

            if(tmp < 0)
            {
                while(tmp < 0)
                    tmp += n;
            }
            cnt += tmp;

            sb.append(1 + " " + (i+1) + " " + tmp + "\n");
        }

        out.println(n+1);

        out.print(sb);

        out.println(2 + " " + n + " " + (n));

        out.flush();
        out.close();

    }

}