Every day Kotlin heroes analyze the statistics of their website. For n days, they wrote out n numbers a_1, a_2, ..., a_n, where a_i is the number of visits on the i-th day.

They believe that a day is bad if there are at least 2 days before it with a strictly greater number of visits. For example, if n=8 and a=[3, 1, 4, 1, 5, 9, 2, 6], then the day 4 is bad (because a_4=1, but there are a_1=3 and a_3=4). Also, the day with the number 7 is bad too.

Write a program that finds the number of bad days.

Input

The first line contains an integer n (1 ≤ n ≤ 2⋅10^5), where n is the number of days. The second line contains n positive integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9), where a_i is the number of website visits on the i-th day.

Output

Print the number of bad days, i.e. such days that there are at least two days before it with a strictly greater number of visits.

Examples

Input


8
3 1 4 1 5 9 2 6


Output


2


Input


5
1 1 1 1 1


Output


0


Input


13
2 7 1 8 2 8 1 8 2 8 4 5 9


Output


6

Source: codeforces | Difficulty: UNKNOWN_DIFFICULTY
Tags: Implementation


Solutions: