Inversion Sorting

There is a hidden permutation a_1, a_2,\dots, a_n of integers 1, 2,\dots, n. Your task is to sort the permutation by reversing subarrays. On each turn, you can reverse a subarray of the permutation. After that, you will be reported the number of inversions in the permutation. If the number of inversions is 0 (i.e., the permutation is sorted), you win. Interaction This is an interactive problem. Your code will interact with the grader using standard input and output. You should start by reading a single integer n: the length of the permutation. On your turn, print two integers i and j: reverse the subarray between indices i and j. After this, the next input line has a single integer: the number of inversions after the operation. If the number is 0, you win and your program must terminate after this.

Constraints

$1\leq n\leq 1000$

$you can make at most 4n operations$

Example

3 1 2 1 2 3 0

Explanation: Here the initial permutation is [3,1,2]. After the first operation the permutation is [1,3,2] and the number of inversions is 1. After the second operation the permutation is [1,2,3] and the number of inversions is 0.