~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 < \dots < T_i > T_{i+1} > \dots > 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\%~ of test cases, ~n \le 20~.

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