题目描述

Some of Farmer John's $N$ cows $(1 ≤ N ≤ 80,000)$ are having a bad hair day! Since each cow is self-conscious about her messy hairstyle, FJ wants to count the number of other cows that can see the top of other cows' heads.

Each cow i has a specified height $h_i$ $(1 ≤ h_i ≤ 1,000,000,000)$ and is standing in a line of cows all facing east (to the right in our diagrams). Therefore, cow i can see the tops of the heads of cows in front of her (namely cows $i+1$, $i+2$, and so on), for as long as these cows are strictly shorter than cow $i$.

Consider this example:

-
-       -
-   -   -
-   -   -
- - - - -
- - - - - -
1 2 3 4 5 6

Cows facing right -->

Cow #1 can see the hairstyle of cows #2, 3, 4.
Cow #2 can see no cow's hairstyle.
Cow #3 can see the hairstyle of cow #4.
Cow #4 can see no cow's hairstyle.
Cow #5 can see the hairstyle of cow 6.
Cow #6 can see no cows at all!

Let $c_i$ denote the number of cows whose hairstyle is visible from cow $i$; please compute the sum of $c_1$ through $c_N$. For this example, the desired is answer $3 + 0 + 1 + 0 + 1 + 0 = 5$.

输入格式

Line 1: The number of cows, $N$.

Lines 2..$N+1$: Line $i+1$ contains a single integer that is the height of cow $i$.

输出格式

Line 1: A single integer that is the sum of $c_1$ through $c_N$.

6
10
3
7
4
12
2

5