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 javafx.scene.input.InputMethodTextRun;
import org.omg.CORBA.INTERNAL;
import sun.rmi.server.Activation$ActivationSystemImpl_Stub;

import java.io.*;
import java.math.BigInteger;
import java.text.DecimalFormat;
import java.util.*;

public class Newbie {

    static InputReader sc = new InputReader(System.in);
    static PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) {
        solver s = new solver();
        long t = 1;
        while (t > 0) {
            s.solve();
            t--;
        }
        out.close();
    }

   /* static class descend implements Comparator<pair1> {
        public int compare(pair1 o1, pair1 o2) {
            if (o1.pop != o2.pop)
                return (int) (o1.pop - o2.pop);
            else
                return o1.in - o2.in;
        }
    }*/

    static class InputReader {
        public BufferedReader br;
        public StringTokenizer token;

        public InputReader(InputStream stream) {
            br = new BufferedReader(new InputStreamReader(stream), 32768);
            token = null;
        }

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

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

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

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

    static class card {
        long a;
        int cnt;
        int i;

        public card(long a, int cnt, int i) {
            this.a = a;
            this.cnt = cnt;
            this.i = i;
        }
    }

    static class ascend implements Comparator<pair> {
        public int compare(pair o1, pair o2) {
            if (o1.a != o2.a)
                return (int) (o1.a - o2.a);
            else
                return o1.b - o2.b;
        }
    }

    static class extra {

        static boolean v[] = new boolean[100001];
        static List<Integer> l = new ArrayList<>();
        static int t;

        static void shuffle(long a[]) {
            List<Long> l = new ArrayList<>();
            for (int i = 0; i < a.length; i++)
                l.add(a[i]);
            Collections.shuffle(l);
            for (int i = 0; i < a.length; i++)
                a[i] = l.get(i);
        }

        static int gcd(int a, int b) {
            if (b == 0)
                return a;
            else
                return gcd(b, a % b);
        }

        static boolean valid(int i, int j, int r, int c, char ch[][]) {
            if (i >= 0 && i < r && j >= 0 && j < c && ch[i][j] != '#') {
                // System.out.println(i+" /// "+j);
                return true;
            } else {
                //  System.out.println(i+" //f "+j);
                return false;
            }
        }

        static void seive() {
            for (int i = 2; i < 100001; i++) {
                if (!v[i]) {
                    t++;
                    l.add(i);
                    for (int j = 2 * i; j < 100001; j += i)
                        v[j] = true;
                }
            }
        }

        static int binary(LinkedList<Integer> a, long val, int n) {
            int mid = 0, l = 0, r = n - 1, ans = 0;
            while (l <= r) {
                mid = (l + r) >> 1;
                if (a.get(mid) == val) {
                    r = mid - 1;
                    ans = mid;
                } else if (a.get(mid) > val)
                    r = mid - 1;
                else {
                    l = mid + 1;
                    ans = l;
                }
            }
            return (ans + 1);
        }

        static long fastexpo(int x, int y) {
            long res = 1;
            while (y > 0) {
                if ((y & 1) == 1) {
                    res *= x;
                }
                y = y >> 1;
                x = x * x;
            }
            return res;
        }

        static long lfastexpo(long x, long y, long p) {
            long res = 1;
            x = x % p;
            while (y > 0) {
                if ((y & 1) == 1) {
                    res = (res * x) % p;
                }
                y = y >> 1;
                x = (x * x) % p;
            }
            return res;
        }

       /* void dijsktra(int s, List<pair> l[], int n) {
            PriorityQueue<pair> pq = new PriorityQueue<>(new ascend());
            int dist[] = new int[100005];
            boolean v[] = new boolean[100005];
            for (int i = 1; i <= n; i++)
                dist[i] = 1000000000;
            dist[s] = 0;
            for (int i = 1; i < n; i++) {
                if (i == s)
                    pq.add(new pair(s, 0));
                else
                    pq.add(new pair(i, 1000000000));
            }
            while (!pq.isEmpty()) {
                pair node = pq.remove();
                v[node.a] = true;
                for (int i = 0; i < l[node.a].size(); i++) {
                    int v1 = l[node.a].get(i).a;
                    int w = l[node.a].get(i).b;
                    if (v[v1])
                        continue;
                    if ((dist[node.a] + w) < dist[v1]) {
                        dist[v1] = dist[node.a] + w;
                        pq.add(new pair(v1, dist[v1]));
                    }
                }
            }
        }*/
    }

    static class pair {
        long a;
        int b;

        public pair(long a, int i) {
            this.a = a;
            this.b = i;
        }
    }

    static class pair1 {
        pair p;
        int in;

        public pair1(pair a, int n) {
            this.p = a;
            this.in = n;
        }
    }


    static int inf = 5000013;

    static class solver {
        DecimalFormat df = new DecimalFormat("0.000000000");
        extra e = new extra();
        long mod = 1000000007;

        void solve() {
            int n = sc.nextInt();
            int a[]=new int[n];
            for(int i=0;i<n;i++)
            {
                a[i]=sc.nextInt();
            }
            int sum=0;
            System.out.println((n+1));
            for (int i=n-1;i>=0;i--)
            {
                long t=((i-(a[i]+sum)%n+n))%n;
                System.out.println(1+ " "+(i+1)+" "+(t));
                sum+=t;
            }
            System.out.println(2+" "+n+" "+n);
        }
    }
}