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(input())
A=[int(i) for i in input().split()]
def f(A):
    P=[0]*(N+1)
    S=[(-1,0)]
    for i,a in enumerate(A):
        while S[-1][1]>a:
            S.pop()
        t=i-S[-1][0]
        P[a]=t
        S.append((i,a))
    return P
P=f(A)
Q=f(A[::-1])
print(sum(a*P[a]*Q[a] for a in A))