Description

$N$ students stand in a row, and the music teacher needs to ask $(N-K)$ of them to step out of the line, leaving the remaining $K$ students to form a chorus formation.

A chorus formation is defined as follows: Let the $K$ students be numbered from left to right as $1, 2, \dots, K$, with their respective heights being $T_1, T_2, \dots, T_K$. Their heights must satisfy $T_1 < T_2 < \dots < T_i$ and $T_i > T_{i+1} > \dots > T_K$ for some $i$ where $1 \leq i \leq K$.

Your task is, given the heights of all $N$ students, to calculate the minimum number of students who need to step out so that the remaining students can form a chorus formation.

Input Format

The first line of input is an integer $N$ ($2 \leq N \leq 100$), representing the total number of students.
The second line contains $N$ integers separated by spaces, where the $i$-th integer $T_i$ ($130 \leq T_i \leq 230$) is the height (in centimeters) of the $i$-th student.

Output Format

The output consists of a single line containing one integer, which is the minimum number of students who need to step out.

8
186 186 150 200 160 130 197 220

4

Hint

For 50% of the test cases, it is guaranteed that n ≤ 20; for all test cases, it is guaranteed that n ≤ 100.