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 Python (3.4.3) (judge verdict: Accepted)

class UnionFind():
    def __init__(self,size):
        self.table=[-1]*size
    def root(self,x):
        while self.table[x]>=0:
            x=self.table[x]
        return x
    def unite(self,x,y):
        s1=self.root(x)
        s2=self.root(y)
        if s1!=s2:
            if self.table[s1]>self.table[s2]:
                s1,s2=s2,s1
            self.table[s1]+=self.table[s2]
            self.table[s2]=s1
        return
    def same(self,x,y):
        return self.root(x)==self.root(y)
    def size(self,x):
        return -self.table[self.root(x)]
n,*a=map(int,open(0).read().split())
u=UnionFind(n)
b=[0]*n
for i,t in enumerate(a):b[t-1]=i
c=0
for k in b[::-1]:
    l=r=1
    if k>0 and a[k-1]>a[k]:
        l+=u.size(k-1)
        u.unite(k-1,k)
    if k+1<n and a[k+1]>a[k]:
        r+=u.size(k+1)
        u.unite(k+1,k)
    c+=l*r*a[k]
print(c)