There are stacks numbered from to . Initially, there are integers in the first stack, while the second stack and the third stack are empty. Each time you can choose two stacks and , and pop an integer from the top of the -th stack, and then push it on the top of the -th stack. Now your task is to sort the numbers with no more than operations. That is to say, after all operations, all the numbers are in the first stack in non-decreasing order from top to bottom.

输入描述:

The first line of input contains an integer , denoting the number of integers.
The second line contains  integers , denoting the numbers in the first stack from bottom to top. ( is the bottom and  is the top)

输出描述:

The first line of output contains an integer , denoting the number of operations.
In the next  lines, each line contains two integers  and , denoting an operation. You must guarantee that the -th stack is not empty when you choose it.
If there are multiple solutions, you can print any one of them.

2
100 200

4
1 2
1 3
2 1
3 1

3
200 300 100

6
1 2
1 3
1 2
3 1
2 1
2 1