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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
Let c[i] denote the number of cows whose hairstyle is visible from cow i; please compute the sum of c through c[N]. For this example, the desired is answer 3 + 0 + 1 + 0 + 1 + 0 = 5.
6 10 3 7 4 12 2