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.ArrayList;
import java.util.List;
import java.util.Scanner;

public class UnderDiagonalSolver {

    private int n;

    private List<Pair> p;

    private List<Action> a;

    private int z;

    public static void main(String[] args) {
        UnderDiagonalSolver solver = new UnderDiagonalSolver();

        solver.readData();
        solver.solve();

        StringBuilder builder = new StringBuilder();
        for (int i = 0; i < solver.a.size(); i++) {
            builder.append(solver.a.get(i));
            builder.append("\r\n");
        }
        System.out.println(solver.a.size());
        System.out.println(builder);
    }

    private void solve() {
        a = new ArrayList<Action>();

        if (checkResult()) {
            return;
        }

        for (z = 0; z < (n + 1) / 2; z++) {
            int[] rowCount = new int[n];
            for (int i = 0; i < p.size(); i++) {
                Pair pair = p.get(i);

                if (pair.x - 1 >= z && pair.x - 1 < n - z && pair.y - 1 >= z && pair.y - 1 < n - z) {
                    rowCount[p.get(i).x - 1]++;
                }
            }
            int minRowIndex = getMinIndex(rowCount);
            int maxRowIndex = getMaxIndex(rowCount);

            int[] columnCount = new int[n];
            for (int i = 0; i < p.size(); i++) {
                Pair pair = p.get(i);

                if (pair.x - 1 >= z && pair.x - 1 < n - z && pair.y - 1 >= z && pair.y - 1 < n - z) {
                    columnCount[p.get(i).y - 1]++;
                }
            }
            int minColumnIndex = getMinIndex(columnCount);
            int maxColumnIndex = getMaxIndex(columnCount);

            // first row with zero 1
            swapRow(minRowIndex + 1, z + 1);
            // last column with zero 1
            swapColumn(minColumnIndex + 1, n - z);

            // last row with max 1
            swapRow(maxRowIndex == z ? minRowIndex + 1 : maxRowIndex + 1, n - z);
            // first column with max 1
            swapColumn(maxColumnIndex == n - z - 1 ? minColumnIndex + 1 : maxColumnIndex + 1, z + 1);

            if (rowCount[maxRowIndex] == 1 && columnCount[maxColumnIndex] == 1) {
                boolean contains = false;

                for (int i = 0; i < p.size(); i++) {
                    Pair pair = p.get(i);

                    if (pair.x == z && pair.y == n - 1 - z) {
                        contains = true;
                        break;
                    }
                }

                if (contains) {
                    if (z != (n - 2) / 2) {
                        swapRow(n - 1 - z, n - 2 - z);
                    } else {
                        break;
                    }
                }
            }

            if (checkResult()) {
                break;
            }
        }
    }

    private boolean checkResult() {
        boolean result = true;

        for (int i = 0; i < p.size(); i++) {
            Pair pair = p.get(i);

            if (pair.x <= pair.y) {
                result = false;
                break;
            }
        }

        return result;
    }

    private void swapRow(int i, int j) {
        if (i != j) {
            for (int k = 0; k < p.size(); k++) {
                Pair pair = p.get(k);

                if (pair.x == i) {
                    pair.x = j;
                } else if (pair.x == j) {
                    pair.x = i;
                }
            }

            a.add(new Action(1, i, j));
        }
    }

    private void swapColumn(int i, int j) {
        if (i != j) {
            for (int k = 0; k < p.size(); k++) {
                Pair pair = p.get(k);

                if (pair.y == i) {
                    pair.y = j;
                } else if (pair.y == j) {
                    pair.y = i;
                }
            }

            a.add(new Action(2, i, j));
        }
    }

    private int getMinIndex(int[] x) {
        int min = x[z];
        int result = z;

        for (int i = z + 1; i < x.length - z; i++) {
            if (x[i] < min) {
                min = x[i];
                result = i;
            }
        }

        return result;
    }

    private int getMaxIndex(int[] x) {
        int max = x[z];
        int result = z;

        for (int i = z + 1; i < x.length - z; i++) {
            if (x[i] > max) {
                max = x[i];
                result = i;
            }
        }

        return result;
    }

    private void readData() {
        Scanner scanner = new Scanner(System.in);

        n = scanner.nextInt();
        p = new ArrayList<Pair>();

        for (int i = 0; i < n - 1; i++) {
            int x = scanner.nextInt();
            int y = scanner.nextInt();

            p.add(new Pair(x, y));
        }
    }

    private static class Pair {

        private int x;

        private int y;

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

    private static class Action {

        private int t;

        private int i;

        private int j;

        private Action(int t, int i, int j) {
            this.t = t;
            this.i = i;
            this.j = j;
        }

        @Override
        public String toString() {
            return t + " " + i + " " + j;
        }
    }
}