One day, Snuke was given a permutation of length N, a_1, a_2, ..., a_N, from his friend.

Find the following:

<image>

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
#!/usr/bin/env python3
N = int(input())
a = list(map(int, input().split()))

b = [None] * (N + 1)
for i, x in enumerate(a):
    b[x] = i

ans = 0
l_idx = list(range(N + 1))
r_idx = list(range(N + 1))
for i, p in reversed(list(enumerate(b))[1:]):
    l, r = l_idx[p], r_idx[p]
    ans += i * (p - l + 1) * (r - p + 1)
    l_idx[r + 1] = l
    r_idx[l - 1] = r

print(ans)
