B. Bad Days
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Every day Kotlin heroes analyze the statistics of their website. For $$$n$$$ days, they wrote out $$$n$$$ numbers $$$a_1, a_2, \dots, a_n$$$, 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 $$$n$$$ ($$$1 \le n \le 2\cdot10^5$$$), where $$$n$$$ is the number of days. The second line contains $$$n$$$ positive integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$), 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