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 = [-1 for i in range(n)], [n for i in range(n)]
    for i in range(n):
        if i == 0:
            continue
        elif a[i] > a[i-1]:
            l[i] = i - 1
        else:
            idx = l[i-1]
            while idx != -1 and a[i] < a[idx]:
                idx = l[idx]
            l[i] = idx

    for i in range(n-1, -1, -1):
        if i == n-1:
            continue
        elif a[i] > a[i+1]:
            r[i] = i + 1
        else:
            idx = r[i+1]
            while idx != n and a[i] < a[idx]:
                idx = r[idx]
            r[i] = idx

    ans = 0
    for i in range(n):
        ans += a[i] * (i-l[i]) * (r[i]-i)

    print(ans)


if __name__ == '__main__':
    main()
