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, = map(int, input().split())
indices = {a: i for i, a in enumerate(A)}
left = {i: i for i in range(N)} # "left[i] = l" is equivalent to "A[l], ..., A[i-1] > A[i]"
right = {i: i for i in range(N)} # "right[i] = r" is equivalent to "A[i] < A[i+1], ..., A[r]"
ans = 0
for a in range(N, 0, -1):
    idx = indices[a]
    l, r = left[idx], right[idx]
    ans += (idx - l + 1) * (r - idx + 1) * a
    left[r+1], right[l-1] = l, r # A[l-1] < A[l], ..., A[r] > A[r+1]
print(ans)