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: Time Limit Exceeded)

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

def f(aa)
l=[[0,-1]]
u=[]
N.times{|i|
  a=aa[i]
  b=l.bsearch_index{|x,_|x>a}
  if b
    l=l[0,b]
    l<<[a,i]
    u<<i-l[b-1][1]
  else
    l<<[a,i]
    u<<1
  end
}
u
end

B=f(A)
C=f(A.reverse).reverse
r=0
N.times{|i|
  r+=A[i]*B[i]*C[i]
}
p r