Rooftop Garden Benchmarking

There are $N$ buildings standing in a row in a city. The $i$-th building from the left has height $h_i$.

Every building manager is diligent and wants to benchmark the rooftop gardens of other buildings. Each manager can look only to the right from their own building, so manager $i$ initially wants to see the rooftops of buildings $i+1, i+2, \dots, N$.

The view can be blocked, however. Looking to the right, the moment a manager meets a building whose height is greater than or equal to their own, that building and every building beyond it become invisible. In other words, manager $i$ can only see a consecutive run of strictly shorter buildings, and the view is blocked as soon as the first building of height at least $h_i$ appears (that blocking building is not counted either).

Find the total number of rooftop gardens that all managers can benchmark.

For example, consider $N = 6$ with heights $H = {10, 3, 7, 4, 12, 2}$, illustrated below.

             = 
 =           = 
 =     -     = 
 =     =     =        -> viewing direction
 =  -  =  =  =   
 =  =  =  =  =  = 
10  3  7  4  12 2     -> building heights
[1][2][3][4][5][6]    -> building numbers

• Manager 1 (height 10) sees buildings 2, 3, and 4, but building 5 (height 12) is at least as tall, so the view stops there. → 3
• Manager 2 (height 3) is blocked immediately by building 3 (height 7). → 0
• Manager 3 (height 7) sees only building 4 and is blocked by building 5 (height 12). → 1
• Manager 4 (height 4) is blocked immediately by building 5 (height 12). → 0
• Manager 5 (height 12) sees only building 6. → 1
• Manager 6 is the last building and has nothing to look at. → 0

Therefore the total is $3 + 0 + 1 + 0 + 1 + 0 = 5$.

• The first line contains the number of buildings $N$. ($1 \le N \le 80000$)
• Each of the next $N$ lines contains one building height $h_i$. ($1 \le h_i \le 10^9$)

• Print, on a single line, the total number of rooftop gardens (buildings) that all managers can benchmark.