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
from collections import defaultdict, Counter
from itertools import product, groupby, count, permutations, combinations
from math import pi, sqrt
from collections import deque
from bisect import bisect, bisect_left, bisect_right
INF = float("inf")


def main():
    N = int(input())
    a = list(map(int, input().split()))

    idx = {}
    for i in range(N):
        idx[a[i]] = i

    ans = 0
    left_idx, right_idx = list(range(N + 2)), list(range(N + 2))
    for a in range(N, 0, -1):
        i = idx[a]
        l, r = left_idx[i], right_idx[i]

        ans += a * (i - l + 1) * (r - i + 1)
        left_idx[r + 1] = l
        right_idx[l - 1] = r

    print(ans)


if __name__ == '__main__':
    main()
