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문제

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:

        =
=       =
=   -   =           Cows facing right -->
=   =   =
= - = = =
= = = = = =
1 2 3 4 5 6
  • 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.

입력

  • 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.

 

출력

  • Line 1: A single integer that is the sum of c[1] through c[N].

예제 입력

6
10
3
7
4
12
2

예제 출력

5

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