1407C · Chocolate Bunny

Problem: This is an interactive problem.

We hid from you a permutation $p$ of length $n$, consisting of the elements from $1$ to $n$. You want to guess it. To do that, you can give us 2 different indices $i$ and $j$, and we will reply with $p_{i} \bmod p_{j}$ (remainder of division $p_{i}$ by $p_{j}$).

We have enough patience to answer at most $2 \cdot n$ queries, so you should fit in this constraint. Can you do it?

As a reminder, a permutation of length $n$ is an array consisting of $n$ distinct integers from $1$ to $n$ in arbitrary order. For example, $[2,3,1,5,4]$ is a permutation, but $[1,2,2]$ is not a permutation ($2$ appears twice in the array) and $[1,3,4]$ is also not a permutation ($n=3$ but there is $4$ in the array).

Input Format: The only line of the input contains a single integer $n$ ($1 \le n \le 10^4$) — length of the permutation.