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Time Limit: 1.0 s

Memory Limit: 128.0 MB

Description

A curious kid loves playing with numbers. One day, he invents a fun game using a list of numbers. He calls a number in the list 'special' if it follows at least one of these two rules:

• There are at least a[i] numbers greater or equal than a[i] on its right.
• There are at least a[i] numbers smaller or equal than a[i] on its left.

The kid wants to know how many numbers in the list are special.

Can you help him figure it out?

Input

• The first line contains an integer n (1 ≤ n ≤ 10⁵) — the number of elements in the list.
• The second line contains n space-separated integers a₁, a₂, ..., aₙ (0 ≤ a[i] ≤ n−1) — the elements of the list.

Output

• Print a single integer — the number of special numbers in the list.

Sample

6
1 1 3 1 5 1

4