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
input()
A=map(int,raw_input().split())
def f():
 s=[(0,-1)];p=A*2
 for i,a in enumerate(A):
  while a<s[-1][0]:s.pop()
  p[a]=i-s[-1][1];s+=[(a,i)]
 return p
l=f()
A.reverse()
r=f()
print sum(a*l[a]*r[a]for a in A)