Problem:
Score : 400 points

Problem Statement

One day, Snuke was given a permutation of length N, a_1, a_2, ..., a_N, from his friend.

Find the following:

Constraints

1 ≦ N ≦ 200,000

(a_1, a_2, ..., a_N) is a permutation of (1, 2, ..., N).

Input

The input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the answer.

Note that the answer may not fit into a 32-bit integer.

Sample Input 1

3
2 1 3

Sample Output 1

9

Sample Input 2

4
1 3 2 4

Sample Output 2

19

Sample Input 3

8
5 4 8 1 2 6 7 3

Sample Output 3

85

Solution in Ruby (2.3.3) (judge verdict: Runtime Error)

def count(l,r)
  (r-l+1)*(r-l+2)/2
end

def dfs(l,r,i)
  return 0 unless 0 <= l
  return 0 unless r < N
  return 0 unless i < N
  return dfs(l,r,i+1) unless l<=@i[i] && @i[i]<=r
  n=count(l,r)
  n-=count(l, @i[i]-1)
  n-=count(@i[i]+1, r)
  dfs(l, @i[i]-1, i+1) + A[@i[i]]*n + dfs(@i[i]+1, r, i+1)
end

N=gets.to_i
A=gets.split.map &:to_i

@i=[0]*N
N.times do |i|
  @i[A[i]-1]=i
end

p dfs(0,N-1,0)