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.*;
import java.util.*;

public class C
{
    InputReader in;
    PrintWriter out;

    void run() throws IOException
    {
        in = new InputReader(System.in);
        out = new PrintWriter(new OutputStreamWriter(System.out));
        solve();
        out.flush();
    }

    public static void main(String[] args) throws IOException
    {
        new C().run();
    }
    int a[][],n;
    int cols[], rows[]; //count of no of 1's
    StringBuilder ans;
    int numOps;
    void solve() throws IOException
    {
        n = in.readInt();
        a = new int[n][n];
        cols = new int[n];
        rows = new int[n];
        for (int i = 0; i < n-1; i++)
        {
            int x = in.readInt()-1;
            int y = in.readInt()-1;
            a[x][y] = 1;
            cols[y]++;
            rows[x]++;
        }
        ans = new StringBuilder();
        func(n);
        out.println(numOps);
        out.println(ans);
    }

    private void func(int n)
    {
        if(n==1)
            return;
        
        //now n-1 1's therefore at least 1 col with no 1, we put it at the last
        //definitely swap will occur
        for (int i = 0; i < n-1; i++)
        {
            if(cols[i]==0)
            {
                //swap ith col with nth col
                ans.append("2 "+(i+1)+" "+n+"\n");
                numOps++;
                swapCol(i,n-1);
                break; 
            }
        }
//        for (int i = 0; i < n; i++)
//        {
//            out.print(Arrays.toString(a[i]));
//            out.println(" "+rows[i]+" "+cols[i]);
//        }
        //place a row containing any 1 at the end row(if one exists) 
        //if swap doesnt occur we swap nth row with itself
        for (int i = 0; i < n-1; i++)
        {
            if(rows[i]>0)
            {
                //swap ith row with nth row
                ans.append("1 "+(i+1)+" "+n+"\n");
                numOps++;
                swapRow(i,n-1);
                break; 
            }
        }
//        for (int i = 0; i < n; i++)
//        {
//            out.print(Arrays.toString(a[i]));
//            out.println(" "+rows[i]+" "+cols[i]);
//        }
        //now problem reduced to n-1 dimension
        //since the nth row and nth col are now not part of the board, adjust cols and rows array
        for (int i = 0; i < n; i++)
        {
            if(a[n-1][i]==1)
                cols[i]--;
            if(a[i][n-1]==1)
                rows[i]--;
        }
        func(n-1);
    }

    private void swapRow(int i, int j)
    {
        int t = rows[i];
        rows[i] = rows[j];
        rows[j] = t;
        
        int t2[] = a[i];
        a[i] = a[j];
        a[j] = t2;
    }

    private void swapCol(int i, int j)
    {
        int t = cols[i];
        cols[i] = cols[j];
        cols[j] = t;
        
        for (int ix = 0; ix < n; ix++)
        {
            int t2 = a[ix][i];
            a[ix][i] = a[ix][j];
            a[ix][j] = t2;
        }
    }
}

class InputReader
{
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

    public InputReader(InputStream stream)
    {
        this.stream = stream;
    }

    public int read()
    {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars)
        {
            curChar = 0;
            try
            {
                numChars = stream.read(buf);
            }
            catch (IOException e)
            {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    public int readInt()
    {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-')
        {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do
        {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public String readString()
    {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuffer res = new StringBuffer();
        do
        {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }

    public Long readLong()
    {
        return Long.parseLong(readString());
    }

    public Double readDouble()
    {
        return Double.parseDouble(readString());
    }

    public static boolean isSpaceChar(int c)
    {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }
}