Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
C. Below the Diagonal

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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:

- Swap
*i*-th and*j*-th rows of the matrix; - 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 *x*_{k}, *y*_{k} (1 ≤ *x*_{k}, *y*_{k} ≤ *n*), separated by a space. A pair (*x*_{k}, *y*_{k}) means that the cell, which is located on the intersection of the *x*_{k}-th row and of the *y*_{k}-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* ≤ 10^{5}) — 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 10^{5}. 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

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/17/2021 23:39:13 (j2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|