You have an array of $N$ integers, $a_1,a_2,\dots ,a_N$. The indices are considered modulo $N$, so $a_{N+1}=a_1,a_{N+2}=a_2,\dots$. Also, $N=4k+2$ for some natural number $k$. You are allowed the following operation: choose index $i$ and then set $a_i$ to be the median of $a_{i+k+1},a_{i+k+2},a_{i+k+3},\dots ,a_{i+3k+1}$ (note that there are an odd number of numbers in this list). Can you perform a series of these operations so that all the elements become equal?

Unfortunately, this is often impossible. So you will be allowed to cheat a little! At any point in time, you can choose an index $i$ and change $a_i$ to any number from $1$ to $N$. However, you are only allowed to do this second operation up to $10$ times. Can you make all the elements equal?

Constraints

$1\le N\le 500$
You are allowed up to $2500$ operations in total, for each test case.

Subtask 1 [30%]

$1\le a_i\le 2$

Subtask 2 [70%]

$1\le a_i\le N$

Input Specification

The first line contains a single integer, $N$.
The next line contains $N$ space-separated integers, $a_1,a_2,\dots ,a_N$.

Output Specification

On the first line, output the number of operations used. This number must not exceed $2500$.
On the remaining lines, print out your operations in order.
For the first operation, output 1 i on a line, to indicate using the operation on index $i$.
For the second operation, output 2 i v on a line, to indicate using the operation on index $i$ to change $a_i$ to $v$, which must be between $1$ and $N$. You may use the second operation at most $10$ times.

Sample Input 1

6
3 4 4 2 5 1

Sample Output 1

4
2 1 4
2 4 4
2 5 4
2 6 4

Explanation for Sample 1

The array after each change is

4 4 4 2 5 1
4 4 4 4 5 1
4 4 4 4 4 1
4 4 4 4 4 4

The second operation is used only $4$ times so this is valid.

Sample Input 2

6
3 4 4 2 5 1

Sample Output 2

5
1 3
1 5
1 4
1 2
1 6

Explanation for Sample 2

For the first operation, $a_3$ becomes the median of $5,1,3$. So the array becomes

3 4 3 2 5 1

For the next operation, $a_5$ becomes the median of $3,4,3$. So the array becomes

3 4 3 2 3 1

In the third operation, $a_4$ becomes the median of $1,3,4$. So the array becomes

3 4 3 3 3 1

And in the final two operations, the array becomes

3 3 3 3 3 1
3 3 3 3 3 3