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()))
l = [0] * (n + 1)
l2 = list(range(n + 2))
l3 = list(range(n + 2))
ans = 0
for i in range(n):
    l[a[i]] = i
for i in range(1, n + 1)[::-1]:
    x, y = l2[l[i]], l3[l[i]]
    ans += (l[i] - x + 1) * (y - l[i] + 1) * i
    l2[y + 1], l3[x - 1] = x, y
print(ans)