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,*a=`dd`.split.map &:to_i;l,r=[a,a.reverse].map{|b|s=[[n=0,i=-1]];r=b*2;b.map{|e|i+=1;s.pop while e<s[-1][0];r[e]=i-s[-1][1];s<<[e,i]};r};a.map{|e|n+=e*l[e]*r[e]};p n