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 ~2\,500~ 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 ~2\,500~.
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