Problem: As meticulous Gerald sets the table and caring Alexander sends the postcards, Sergey makes snowmen. Each showman should consist of three snowballs: a big one, a medium one and a small one. Sergey's twins help him: they've already made n snowballs with radii equal to r1, r2, ..., rn. To make a snowman, one needs any three snowballs whose radii are pairwise different. For example, the balls with radii 1, 2 and 3 can be used to make a snowman but 2, 2, 3 or 2, 2, 2 cannot. Help Sergey and his twins to determine what maximum number of snowmen they can make from those snowballs.

Input

The first line contains integer n (1 ≤ n ≤ 105) — the number of snowballs. The next line contains n integers — the balls' radii r1, r2, ..., rn (1 ≤ ri ≤ 109). The balls' radii can coincide.

Output

Print on the first line a single number k — the maximum number of the snowmen. Next k lines should contain the snowmen's descriptions. The description of each snowman should consist of three space-separated numbers — the big ball's radius, the medium ball's radius and the small ball's radius. It is allowed to print the snowmen in any order. If there are several solutions, print any of them.

Examples

Input

7
1 2 3 4 5 6 7


Output

2
3 2 1
6 5 4


Input

3
2 2 3


Output

0

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class C {

	private static void solve() throws IOException {
		int n = nextInt();
		int[] r = new int[n];
		for (int i = 0; i < n; i++) {
			r[i] = nextInt();
		}
		Arrays.sort(r);
		List<Ball> balls = new ArrayList<Ball>();
		int last = -1;
		for (int i = 0; i < n; i++) {
			if (i == n - 1 || r[i] != r[i + 1]) {
				balls.add(new Ball(r[i], i - last));
				last = i;
			}
		}
		PriorityQueue<Ball> queue = new PriorityQueue<Ball>();
		queue.addAll(balls);
		List<Snowman> answer = new ArrayList<Snowman>();
		while (queue.size() >= 3) {
			Ball b1 = queue.poll();
			Ball b2 = queue.poll();
			Ball b3 = queue.poll();
			answer.add(new Snowman(b1.r, b2.r, b3.r));
			for (Ball b : new Ball[] { b1, b2, b3 }) {
				--b.count;
				if (b.count > 0) {
					queue.add(b);
				}
			}
		}
		out.println(answer.size());
		for (Snowman s : answer) {
			out.println(s.r3 + " " + s.r2 + " " + s.r1);
		}
	}

	static class Ball implements Comparable<Ball> {
		int r, count;

		public Ball(int r, int count) {
			this.r = r;
			this.count = count;
		}

		@Override
		public int compareTo(Ball o) {
			return o.count - count;
		}
	}

	static class Snowman {
		final int r1, r2, r3;

		public Snowman(int r1, int r2, int r3) {
			if (r1 > r2) {
				int t = r1;
				r1 = r2;
				r2 = t;
			}
			if (r1 > r3) {
				int t = r1;
				r1 = r3;
				r3 = t;
			}
			if (r2 > r3) {
				int t = r2;
				r2 = r3;
				r3 = t;
			}
			this.r1 = r1;
			this.r2 = r2;
			this.r3 = r3;
		}
	}

	public static void main(String[] args) {
		try {
			br = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
			solve();
			out.close();
		} catch (Throwable e) {
			e.printStackTrace();
			System.exit(239);
		}
	}

	static BufferedReader br;
	static StringTokenizer st;
	static PrintWriter out;

	static String nextToken() throws IOException {
		while (st == null || !st.hasMoreTokens()) {
			String line = br.readLine();
			if (line == null) {
				return null;
			}
			st = new StringTokenizer(line);
		}
		return st.nextToken();
	}

	static int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	static long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

	static double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}
}