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.util.*;


public class C163 {
	
	class Line{
		public ArrayList<Integer> l = new ArrayList<Integer>();
		public int yuan;

		public Line() {
			l = new ArrayList<Integer>();
		}
		
		
	}
	
	class Lie{
		public int min;
		public int shu;
		public int yuan;
		public Lie(int min, int shu, int yuan) {
			super();
			this.min = min;
			this.shu = shu;
			this.yuan = yuan;
		}
		
		
	}
	
	class Jl{
		public int a,b,c;

		public Jl(int a, int b, int c) {
			super();
			this.a = a;
			this.b = b;
			this.c = c;
		}

		@Override
		public String toString() {
			return String.format("%d %d %d", a,b,c);
		}
		
	}
	
	Line maz[] ;
	Lie lie[];
	int juzhen[][];
	
	List <Jl> ans = new LinkedList<Jl>();
	
	void run(){
		
		Scanner cin = new Scanner(System.in);
		int n = cin.nextInt();
		maz = new Line[n+1];
		
		int i,j;
		for(i=0;i<n+1;i++){
			maz[i] = new Line();
			maz[i].yuan = i;
		}
		maz[0].yuan = 0;
		for(i=0;i<n-1;i++){
			int x = cin.nextInt();
			int y = cin.nextInt();
			maz[x].l.add(y);
		}
		
		Arrays.sort(maz,new Comparator<Line>() {

			@Override
			public int compare(Line o1, Line o2) {
				if(o1.l.size() != o2.l.size())
					return o1.l.size() - o2.l.size();
				return o1.yuan - o2.yuan;
			}
			
		});
		
		int bi[] = new int[n+1];
		
		for(i=0;i<=n;i++)
			bi[maz[i].yuan] = i;
		for(i=n;i>=1;i--){
			if(i != bi[i])
			{
				int w = i;
				for(j=1;j<=n;j++)
				{
					if(bi[j] == i)
						w = j;
				}
				ans.add(new Jl(1,i,w));
				int temp = bi[i];
				bi[i] = bi[w];
				bi[w] = temp;
			}
		}
		
		
		
		
		juzhen = new int[n+1][n+1];
		for(i=1;i<=n;i++){
			for(j=1;j<=n;j++)
				juzhen[i][j] = 0;
		}
		for(i=n;i>=1;i--){
			if(maz[i].l.size() == 0)
				break;
			for(j=0;j<maz[i].l.size();j++)
			{
				juzhen[i][maz[i].l.get(j)] = 1;
			}
		}
		
		lie = new Lie[n+1];
		
		lie[0] = new Lie(-9,90000,-9);
		
		for(j=1;j<=n;j++){
			
			boolean flag = false;
			int count = 0;
			int min = -1;
			for(i=1;i<=n;i++){
				if(juzhen[i][j] == 1 && flag == false)
				{
					flag =true;
					min = i;
					count ++;
				}
				else if(juzhen[i][j] == 1){
					count ++;
				}
			}
			lie[j] = new Lie(min, count,j);
		}
		
		Arrays.sort(lie,new Comparator<Lie>() {

			@Override
			public int compare(Lie o1, Lie o2) {
				
				if(o1.shu != o2.shu)
				{
					return o2.shu - o1.shu;
				}
				return o1.min - o2.min;
			}
			
		});
		
		
		for(i=1;i<=n;i++)
			bi[lie[i].yuan] = i;
		
		for(i=n;i>=1;i--){
			if(i != bi[i])
			{
				int w = i;
				for(j=1;j<=n;j++)
				{
					if(bi[j] == i)
						w = j;
				}
				ans.add(new Jl(2,i,w));
				int temp = bi[i];
				bi[i] = bi[w];
				bi[w] = temp;
			}
		}
		
		System.out.println(ans.size());
		for(Jl buf : ans){
			System.out.println(buf);
		}
	}
	
	
	
	
	public static void main(String[] args) {
		
		new C163().run();
	}
}