$N$ students stand in a row, and the music teacher asks $N-K$ students to leave so that the remaining $K$ students form a chorus formation.

The chorus formation refers to such a formation: Suppose the $K$ students left are numbered $1,2,\dots ,K$ from left to right, and their heights are $T_1,T_2,\dots ,T_K$ respectively, then their heights satisfy $T_1<\cdots <T_i>T_{i+1}>\cdots >T_K$ $(1\le i\le K)$.

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

Input Specification

The first line of the input consists of an integer $N$ $(2\le N\le 100)$ denoting the number of students. The second line consists of $n$ integers separated by a single space denoting the height of the $i$-th student. The heights satisfy $130\le T_i\le 230$.

Output Specification

Output the minimum number of students that should leave to form a chorus formation.

Sample Input

8
186 186 150 200 160 130 197 220

Sample Output

4

Constraints

For $50\mathrm{\%}$ of test cases, $n\le 20$.

For all test cases, $n\le 100$.