Problem: You are given a square matrix consisting of n rows and n columns. We assume that the rows are numbered from 1 to n from top to bottom and the columns are numbered from 1 to n from left to right. Some cells (n - 1 cells in total) of the the matrix are filled with ones, the remaining cells are filled with zeros. We can apply the following operations to the matrix:

  1. Swap i-th and j-th rows of the matrix; 
  2. Swap i-th and j-th columns of the matrix. 



You are asked to transform the matrix into a special form using these operations. In that special form all the ones must be in the cells that lie below the main diagonal. Cell of the matrix, which is located on the intersection of the i-th row and of the j-th column, lies below the main diagonal if i > j.

Input

The first line contains an integer n (2 ≤ n ≤ 1000) — the number of rows and columns. Then follow n - 1 lines that contain one's positions, one per line. Each position is described by two integers xk, yk (1 ≤ xk, yk ≤ n), separated by a space. A pair (xk, yk) means that the cell, which is located on the intersection of the xk-th row and of the yk-th column, contains one.

It is guaranteed that all positions are distinct.

Output

Print the description of your actions. These actions should transform the matrix to the described special form.

In the first line you should print a non-negative integer m (m ≤ 105) — the number of actions. In each of the next m lines print three space-separated integers t, i, j (1 ≤ t ≤ 2, 1 ≤ i, j ≤ n, i ≠ j), where t = 1 if you want to swap rows, t = 2 if you want to swap columns, and i and j denote the numbers of rows or columns respectively.

Please note, that you do not need to minimize the number of operations, but their number should not exceed 105. If there are several solutions, you may print any of them.

Examples

Input

2
1 2


Output

2
2 1 2
1 1 2


Input

3
3 1
1 3


Output

3
2 2 3
1 1 3
1 1 2


Input

3
2 1
3 2


Output

0

Solution (in JAVA):

Solution:
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.HashSet;
import java.util.List;
import java.util.Set;
import java.util.StringTokenizer;

public class P266C {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		Task solver = new Task();
		solver.solve(in, out);
		out.close();
	}

	static class Task {

		private class Triplet {
			int x, y, z;

			public Triplet(int x, int y, int z) {
				this.x = x;
				this.y = y;
				this.z = z;
			}

			@Override
			public String toString() {
				return x + " " + y + " " + z;
			}

		}

		private class Pair {
			int x, y;

			public Pair(int x, int y) {
				this.x = x;
				this.y = y;
			}

			@Override
			public String toString() {
				return x + " " + y;
			}

			@Override
			public int hashCode() {
				final int prime = 31;
				int result = 1;
				result = prime * result + x;
				result = prime * result + y;
				return result;
			}

			@Override
			public boolean equals(Object obj) {
				Pair other = (Pair) obj;
				if (x != other.x)
					return false;
				if (y != other.y)
					return false;
				return true;
			}

		}

		public void solve(InputReader in, PrintWriter out) {
			int n = in.nextInt();
			int[] rc = new int[n + 1];
			int[] cc = new int[n + 1];
			Set<Pair> matrix = new HashSet<>();
			int[] swapR = new int[n + 1];
			int[] swapC = new int[n + 1];
			for (int i = 1; i <= n; i++) {
				swapR[i] = i;
				swapC[i] = i;
			}
			for (int i = 0; i < n - 1; i++) {
				int r = in.nextInt();
				int c = in.nextInt();
				rc[r]++;
				cc[c]++;
				matrix.add(new Pair(r, c));
			}
			List<Triplet> sol = new ArrayList<>();
			// loop over size of matrix
			for (int i = n; i > 1; i--) {
				// finding empty column
				int ec = i;
				if (cc[i] != 0) {
					for (int j = 1; j < i; j++) {
						if (cc[j] == 0) {
							ec = j;
							break;
						}
					}
					if (ec != i) {
						// swap to rightmost
						// dont care about cc[i]
						sol.add(new Triplet(2, ec, i));
						cc[ec] = cc[i];
						swapC[ec] = i;
					}
				}
				// finding row with atleast one 1
				int nr = i;
				for (int j = 1; j < i; j++) {
					if (rc[j] > 0) {
						nr = j;
						break;
					}
				}
				if (nr != i) {
					// swap to bottommost
					// dont care about rc[i]
					sol.add(new Triplet(1, nr, i));
					rc[nr] = rc[i];
					// remove ones
					for (int j = 1; j < i; j++) {
						cc[j] -= matrix.contains(new Pair(swapR[nr], swapC[j])) ? 1 : 0;
					}
					swapR[nr] = i;
				}
			}
			out.println(sol.size());
			for (Triplet t : sol) {
				out.println(t);
			}
		}

	}

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

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

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

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

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

		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}

	}

}