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()))
E = [(v, i + 1) for i, v in enumerate(a)]
E.sort(reverse = True)
L = [0] + [i for i in range(N + 1)]
R = [i + 1 for i in range(N + 1)] + [N + 1]
res = 0
for v, i in E:
  l = L[i]
  r = R[i]
  L[r], R[l] = l, r
  res += v * (i - l) * (r - i)
print(res)