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
n = int(input())
a = list(map(int, input().split()))

index = [-1] * (n + 1)
for i, v in enumerate(a):
    index[v] = i

area = [[i, i] for i in range(n + 1)]
result = 0
for i in range(n, 0, -1):
    position = index[i]
    l, r = area[position]
    area[r + 1][0] = l # right
    area[l - 1][1] = r # left
    result += (position - l + 1) * (r - position + 1) * i
print(result)


