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
def main():
    N = int(input())
    A = list(map(int, input().split()))
    L, R = [0] * N, [0] * N
    s = [(-1, -1)]
    for i, a in enumerate(A):
        while s[-1][0] >= a:
            s.pop()
        L[i] = i - s[-1][1]
        s.append((a, i))
    s = [(-1, N)]
    for i in reversed(range(N)):
        a = A[i]
        while s[-1][0] >= a:
            s.pop()
        R[i] = s[-1][1] - i
        s.append((a, i))
    return sum(a * l * r for a, l, r in zip(A, L, R))

print(main())
