Chorus Formation

Problem Background

Special for beginners, ^_^

Problem Description

$N$ students stand in a line. The music teacher wants $(N-K)$ of them to step out, leaving $K$ students forming a chorus formation, while keeping the relative order of all students unchanged.

A chorus formation means: if the $K$ students from left to right are numbered $1,2,\dots,K$ with heights $T_1,T_2,\dots,T_K$, then $T_1\lt T_2\lt\dots\lt T_i,\ T_i\gt T_{i+1}\gt\dots\gt T_K\ (1\le i\le K)$.

Given the heights of all $N$ students, compute the minimum number of students who must step out so that the remaining students form a chorus formation.

Input Format

The first line is an integer $N\ (2\le N\le 100)$ — the total number of students.

The second line contains $N$ integers separated by spaces; the $i$-th integer $T_i\ (130\le T_i\le 230)$ is the height (in cm) of the $i$-th student.

Output Format

Output one line containing a single integer — the minimum number of students who must step out.

Sample Input

8
186 186 150 200 160 130 197 220

Sample Output

4

Constraints

$2\le N\le 100$; $130\le T_i\le 230$.

Time limit 1s, memory limit 1024KiB for each test case.

For $50\%$ of the data, $N\le 20$; for all data, $N\le 100$.