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 cf;

import java.io.BufferedReader;
import java.io.ByteArrayInputStream;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.Random;
import java.util.StringTokenizer;

/**
 * @author Sri Mouli
 * Copyright © 2018 Sri Mouli. All rights reserved.
 */

@SuppressWarnings("ALL")
public class C1088 {

    public static long MOD = 1000000007;
    public static long[][][] dp;
    public static String INPUT = "3 " +
            "0 2 1";

    @SuppressWarnings("unused")
    public static void main(String[] args) {
        long time = System.currentTimeMillis();
        boolean oj = System.getProperty("ONLINE_JUDGE") != null;
        PrintWriter out = new PrintWriter(System.out);
        FastReader in = new FastReader(oj);
        int n = in.nextInt();
        int[]a = in.nextIntArray(n);
        System.out.println(n +1);
        for(int i=n-1;i>=0; i--){

            int t = i-(a[i] % n);
            if(t<0){
                t+=n;
            }
            System.out.println("1 "+ (i+1) + " "+t);
            firstQuery(a,i,t);
        }
        System.out.println("2 "+ n +" "+n);
        secondQuery(a,n);
        
    }

    private static void secondQuery(int[] a, int n) {
        for(int i=0;i<n;i++){
            a[i]%=n;
        }
        //System.out.println("Yo2 "+Arrays.toString(a));
    }

    private static void firstQuery(int[] a, int x, int y) {
        for(int i=0;i<=x;i++){
            a[i]+=y;
        }
        //System.out.println("Yo "+Arrays.toString(a));
    }

    static class FastReader {

        BufferedReader br;
        StringTokenizer st;
        InputStream is;
        byte[] inbuf = new byte[1024];
        int lenbuf = 0, ptrbuf = 0;

        FastReader(boolean onlineJudge) {
            is = onlineJudge ? System.in : new ByteArrayInputStream(INPUT.getBytes());
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }

        FastReader(String file) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(file));
        }

        String next() {

            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

        long nextLong() {
            return Long.parseLong(next());
        }

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

        double nextDouble() {
            return Double.parseDouble(next());
        }

        char nextChar() {
            return next().charAt(0);
        }

        String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }

        int[][] next2DInt(int n, int m) {
            int[][] arr = new int[n][];
            for (int i = 0; i < n; i++) {
                arr[i] = nextIntArray(m);
            }
            return arr;
        }

        long[][] next2DLong(int n, int m) {
            long[][] arr = new long[n][];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLongArray(m);
            }
            return arr;
        }

        int[] shuffle(int[] arr) {
            Random r = new Random();
            for (int i = 1, j; i < arr.length; i++) {
                j = r.nextInt(i);
                arr[i] = arr[i] ^ arr[j];
                arr[j] = arr[i] ^ arr[j];
                arr[i] = arr[i] ^ arr[j];
            }
            return arr;
        }

        int[] uniq(int[] arr) {
            Arrays.sort(arr);
            int[] rv = new int[arr.length];
            int pos = 0;
            rv[pos++] = arr[0];
            for (int i = 1; i < arr.length; i++) {
                if (arr[i] != arr[i - 1]) {
                    rv[pos++] = arr[i];
                }
            }
            return Arrays.copyOf(rv, pos);
        }

    }

}