One day, Snuke was given a permutation of length N, a_1, a_2, ..., a_N, from his friend.

Find the following:

<image>

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()))
    pos = [-1] * (N+1)
    for i in range(N):
        pos[A[i]] = i
    left = list(range(N+2))
    right = list(range(N+2))
    ans = 0
    for i in range(N, 0, -1):
        p = pos[i]
        l = left[p]
        r = right[p]
        ans += i * (p-l+1) * (r-p+1)
        left[r+1] = left[p]
        right[l-1] = right[p]
    print(ans)


if __name__ == "__main__":
    main()
