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():
    import heapq
    N = int(input())
    a = list(map(int, input().split()))
    q = []
    LR = [[0, N-1] for i in range(N)]
    for i in range(N):
        x = a[i]
        while(q and -q[0][0] > x):
            v, id = heapq.heappop(q)
            LR[id][1] = i - 1
        heapq.heappush(q, (-x, i))

    for i in range(N-1, -1, -1):
        x = a[i]
        while(q and -q[0][0] > x):
            v, id = heapq.heappop(q)
            LR[id][0] = i+1
        heapq.heappush(q, (-x, i))
    ans = 0
    for i in range(N):
        ans += a[i] * (LR[i][1] - i + 1)*(i - LR[i][0] + 1)
    print(ans)


main()
