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 third{
public static void main(String[] args)throws IOException {
    FastReader in=new FastReader(System.in);
    StringBuilder sb=new StringBuilder();
    int n=in.nextInt();
    int i,j;
    long pos,x,s;
    long arr[]=new long[n];
    for(i=0;i<n;i++)
    arr[i]=in.nextInt();
    long sum=0;
    sb.append(n+1).append("\n");
    for(i=n-1;i>=0;i--)
    {
        pos=i;
        x=(arr[i]+sum)%n;
        s=(pos-x+n)%n;
        sum+=s;
        sb.append("1 ").append((i+1)+" "+s).append("\n");;
    }
    sb.append("2 "+n+" "+n);
    System.out.println(sb);
}
}
class FastReader {
 
    byte[] buf = new byte[2048];
    int index, total;
    InputStream in;
 
    FastReader(InputStream is) {
        in = is;
    }
 
    int scan() throws IOException {
        if (index >= total) {
            index = 0;
            total = in.read(buf);
            if (total <= 0) {
                return -1;
            }
        }
        return buf[index++];
    }
 
    String next() throws IOException {
        int c;
        for (c = scan(); c <= 32; c = scan());
        StringBuilder sb = new StringBuilder();
        for (; c > 32; c = scan()) {
            sb.append((char) c);
        }
        return sb.toString();
    }
    String nextLine() throws IOException {
        int c;
        for (c = scan(); c <= 32; c = scan());
        StringBuilder sb = new StringBuilder();
        for (; c !=10; c = scan()) {
            sb.append((char) c);
        }
        return sb.toString();
    }
    char nextChar() throws IOException{
        int c;
         for (c = scan(); c <= 32; c = scan());
         return (char)c;
        }
 
    int nextInt() throws IOException {
        int c, val = 0;
        for (c = scan(); c <= 32; c = scan());
        boolean neg = c == '-';
        if (c == '-' || c == '+') {
            c = scan();
        }
        for (; c >= '0' && c <= '9'; c = scan()) {
            val = (val << 3) + (val << 1) + (c & 15);
        }
        return neg ? -val : val;
    }
 
    long nextLong() throws IOException {
        int c;
        long val = 0;
        for (c = scan(); c <= 32; c = scan());
        boolean neg = c == '-';
        if (c == '-' || c == '+') {
            c = scan();
        }
        for (; c >= '0' && c <= '9'; c = scan()) {
            val = (val << 3) + (val << 1) + (c & 15);
        }
        return neg ? -val : val;
    }
}