### Bad Hair Day

Time Limit: 2000 ms
Memory Limit: 65536 KiB

#### Problem Description

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 hi (1 ≤ hi ≤ 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 ci denote the number of cows whose hairstyle is visible from cow i; please compute the sum of c1 through cN.For this example, the desired is answer 3 + 0 + 1 + 0 + 1 + 0 = 5.

Each cow i has a specified height hi (1 ≤ hi ≤ 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 ci denote the number of cows whose hairstyle is visible from cow i; please compute the sum of c1 through cN.For this example, the desired is answer 3 + 0 + 1 + 0 + 1 + 0 = 5.

#### Input

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.

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

#### Output

Line 1: A single integer that is the sum of c

_{1}through c_{N}.#### Sample Input

6 10 3 7 4 12 2

#### Sample Output

5

#### Hint

#### Source

USACO 2006 November Silver