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 $0$.