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

Find the following:

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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.

Examples

Input

3
2 1 3


Output

9


Input

4
1 3 2 4


Output

19


Input

8
5 4 8 1 2 6 7 3


Output

85
n=int(raw_input())
a=map(int,raw_input().split())
def f():
    s=[(0,-1)]
    x=[0]*(n+1)
    for i,j in enumerate(a):
        while s[-1][0]>j:s.pop()
        x[j]=i-s[-1][1]
        s.append((j,i))
    return x
l=f()
a.reverse()
r=f()
print sum([i*l[i]*r[i] for i in a])
