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()))

idx = {A[i]: i for i in range(N)}
 
ans = 0
idx_l, idx_r = list(range(N + 2)), list(range(N + 2))
for a in range(N, 0, -1):
    i = idx[a]
    l, r = idx_l[i], idx_r[i]
    ans += a * (i - l + 1) * (r - i + 1)
    idx_l[r + 1], idx_r[l - 1] = l, r
    
print(ans)