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 = [-1] * N
    s = []
    for i, v in enumerate(a):
        while s and  s[-1][0] > v:
            s.pop()
        if s:
            l[i] = s[-1][1]
        s.append((v, i))
    r = [N] * N
    s = []
    for i, v in (enumerate(reversed(a))):
        while s and s[-1][0] > v:
            s.pop()
        if s:
            r[N - i - 1] = s[-1][1]
        s.append((v, N - i - 1))
    ans = 0
    for i in range(N):
        rr = r[i] - 1
        ll = l[i] + 1
        ans += ((rr - i + 1) * (i - ll) + rr - i)*a[i] + a[i]
    return ans
print(main())
