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
inpl = lambda: list(map(int,input().split()))
def min_len(A):
    N = len(A)
    p = [-1]
    m = [0]
    L = []
    for i in range(N):
        a = A[i]
        while a < m[-1]:
            m.pop()
            p.pop()
        m.append(A[i])
        p.append(i)
        L.append(i-p[-2])
    return L

N = int(input())
A = inpl()
L = min_len(A)
R = min_len(A[::-1])
ans = sum(L[i]*R[N-1-i]*A[i] for i in range(N))
print(ans)