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: Accepted)

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

L = Hash.new
PL = [[0, -1]]

A.each_with_index do |a, i|
  while PL.last[0] > a
    PL.pop
  end

  L[a] = PL.last[1] + 1
  PL << [a, i]
end

R = Hash.new
PR = [[0, -1]]

A.reverse.each_with_index do |a, i|
  while PR.last[0] > a
    PR.pop
  end

  R[a] = PR.last[1] + 1
  PR << [a, i]
end

ans = 0
A.each_with_index do |a, i|
  l = i - L[a] + 1
  r = N - R[a] - i

  ans += a * l * r
end

puts ans