Non-Decreasing Necessity

Given an array of n integers, you are asked to make the array non-decreasing by performing the following operation zero or more times:

Choose any index i (1 ≤ i ≤ n) and replace with any integer.

Your goal is to minimize the number of operations required to make the array non-decreasing.

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 100 000), the length of the array.

The second line contains n space-separated integers (1 ≤ ≤ ).

Output

The program should print a single integer — the minimum number of operations required to make the array non-decreasing.

Examples