Description:
This is an interactive problem.
Homer likes arrays a lot and he wants to play a game with you.
Homer has hidden from you a permutation $$$a_1, a_2, \dots, a_n$$$ of integers $$$1$$$ to $$$n$$$. You are asked to find any index $$$k$$$ ($$$1 \leq k \leq n$$$) which is a local minimum.
For an array $$$a_1, a_2, \dots, a_n$$$, an index $$$i$$$ ($$$1 \leq i \leq n$$$) is said to be a local minimum if $$$a_i < \min\{a_{i-1},a_{i+1}\}$$$, where $$$a_0 = a_{n+1} = +\infty$$$. An array is said to be a permutation of integers $$$1$$$ to $$$n$$$, if it contains all integers from $$$1$$$ to $$$n$$$ exactly once.
Initially, you are only given the value of $$$n$$$ without any other information about this permutation.
At each interactive step, you are allowed to choose any $$$i$$$ ($$$1 \leq i \leq n$$$) and make a query with it. As a response, you will be given the value of $$$a_i$$$.
You are asked to find any index $$$k$$$ which is a local minimum after at most $$$100$$$ queries.
Input Format:
None
Output Format:
None
Note:
In the example, the first line contains an integer $$$5$$$ indicating that the length of the array is $$$n = 5$$$.
The example makes five "?" queries, after which we conclude that the array is $$$a = [3,2,1,4,5]$$$ and $$$k = 3$$$ is local minimum.