Problem:
Score : 700 points

Problem Statement

You are given an integer L. Construct a directed graph that satisfies the conditions below. The graph may contain multiple edges between the same pair of vertices. It can be proved that such a graph always exists.

The number of vertices, N, is at most 20. The vertices are given ID numbers from 1 to N.

The number of edges, M, is at most 60. Each edge has an integer length between 0 and 10^6 (inclusive).

Every edge is directed from the vertex with the smaller ID to the vertex with the larger ID. That is, 1,2,...,N is one possible topological order of the vertices.

There are exactly L different paths from Vertex 1 to Vertex N. The lengths of these paths are all different, and they are integers between 0 and L-1.

Here, the length of a path is the sum of the lengths of the edges contained in that path, and two paths are considered different when the sets of the edges contained in those paths are different.

Constraints

2 \leq L \leq 10^6

L is an integer.

Input

Input is given from Standard Input in the following format:

L

Output

In the first line, print N and M, the number of the vertices and edges in your graph.
In the i-th of the following M lines, print three integers u_i,v_i and w_i, representing the starting vertex, the ending vertex and the length of the i-th edge.
If there are multiple solutions, any of them will be accepted.

Sample Input 1

4

Sample Output 1

8 10
1 2 0
2 3 0
3 4 0
1 5 0
2 6 0
3 7 0
4 8 0
5 6 1
6 7 1
7 8 1

In the graph represented by the sample output, there are four paths from Vertex 1 to N=8:

1 → 2 → 3 → 4 → 8 with length 0

1 → 2 → 3 → 7 → 8 with length 1

1 → 2 → 6 → 7 → 8 with length 2

1 → 5 → 6 → 7 → 8 with length 3

There are other possible solutions.

Sample Input 2

5

Sample Output 2

5 7
1 2 0
2 3 1
3 4 0
4 5 0
2 4 0
1 3 3
3 5 1

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import static java.lang.Math.*;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.InputMismatchException;
import java.util.List;
import java.util.StringTokenizer;

public class Main {

	public static void main(String[] args) throws IOException {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskX solver = new TaskX();
		solver.solve(1, in, out);
		out.close();
	}

	static int INF = 1 << 30;
	static long LINF = 1L << 55;
	static int MOD = 1000000007;
	static int[] mh4 = { 0, -1, 1, 0 };
	static int[] mw4 = { -1, 0, 0, 1 };
	static int[] mh8 = { -1, -1, -1, 0, 0, 1, 1, 1 };
	static int[] mw8 = { -1, 0, 1, -1, 1, -1, 0, 1 };

	static class TaskX {

		public void solve(int testNumber, InputReader in, PrintWriter out) {

			int l = in.nextInt();

			// l 以下の最大の2べきの整数 r を求める
			int r = f(l);

			// 追加するパスの経路数
			int x = l - (int)pow(2, r);

			// 基準のグラフを構築
			List<P> list = new ArrayList<>();
			for (int i = 1; i <= r; i++) {
				list.add(new P(i, i+1, 0));
				list.add(new P(i, i+1, (int)pow(2, i-1)));
			}

			// 値の最大値と構築するノードの情報をもとに辺を構築
			int max = l;
			char[] info = g(r, x).toCharArray();
			for (int i = r; i >= 0; i--) {
				if (info[i] == '0') continue;
				max--;
				int cost = max - ((int)pow(2, i) - 1);
				list.add(new P(i+1, r+1, cost));
				max = cost;
			}

			out.printf("%d %d\n", r+1, list.size());
			for (P p : list) {
				out.println(p);
			}

		}
	}

	static class P {
		int l, r, c;

		public P(int l, int r, int c) {
			super();
			this.l = l;
			this.r = r;
			this.c = c;
		}

		@Override
		public String toString() {
			return l + " " + r + " " + c;
		}
	}

	static int f(int l) {
		int ret = 0;
		int num = 1;
		while (num * 2 <= l) {
			ret++;
			num *= 2;
		}
		return ret;
	}

	static String g(int r, int x) {
		String str = Integer.toBinaryString(x);
		str = String.format("%"+(r+1)+"s", str).replace(" ", "0");
		return reverse(str);
	}

	static String reverse(String str) {
		StringBuilder sb = new StringBuilder();
		sb.append(str);
		return sb.reverse().toString();
	}

	static class InputReader {
		BufferedReader in;
		StringTokenizer tok;

		public String nextString() {
			while (!tok.hasMoreTokens()) {
				try {
					tok = new StringTokenizer(in.readLine(), " ");
				} catch (IOException e) {
					throw new InputMismatchException();
				}
			}
			return tok.nextToken();
		}

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

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

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

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

		public int[] nextIntArrayDec(int n) {
			int[] res = new int[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextInt() - 1;
			}
			return res;
		}

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

		public long[] nextLongArrayDec(int n) {
			long[] res = new long[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextLong() - 1;
			}
			return res;
		}

		public InputReader(InputStream inputStream) {
			in = new BufferedReader(new InputStreamReader(inputStream));
			tok = new StringTokenizer("");
		}
	}

	static long max(long... n) {
		long ret = n[0];
		for (int i = 0; i < n.length; i++) {
			ret = Math.max(ret, n[i]);
		}
		return ret;
	}

	static int max(int... n) {
		int ret = n[0];
		for (int i = 0; i < n.length; i++) {
			ret = Math.max(ret, n[i]);
		}
		return ret;
	}

	static long min(long... n) {
		long ret = n[0];
		for (int i = 0; i < n.length; i++) {
			ret = Math.min(ret, n[i]);
		}
		return ret;
	}

	static int min(int... n) {
		int ret = n[0];
		for (int i = 0; i < n.length; i++) {
			ret = Math.min(ret, n[i]);
		}
		return ret;
	}

}