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()))
a_to_i = {a: i for i, a in enumerate(A, start=1)}

L = [i - 1 for i in range(N + 2)]
R = [i + 1 for i in range(N + 2)]

ans = 0
for a in range(N, 0, -1):
    i = a_to_i[a]
    ans += a * (R[i] - i) * (i - L[i])
    L[R[i]] = L[i]
    R[L[i]] = R[i]

print(ans)