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
#!/usr/bin/env python

from collections import defaultdict

N = int(input())
a = list(map(int, input().split()))

cnt = 0
d = [0] * (N + 2)
for i in range(N):
    d[a[i]] = i


l = list(range(N + 2))
r = list(range(N + 2))

# print(a)
for i in range(N, 0, -1):
    di = d[i]
    cnt += i * (r[di] - di + 1) * (di - l[di] + 1)
    r[l[di] - 1] = r[di]
    l[r[di] + 1] = l[di]
    # print(i)
    # print(r)
    # print(l)
# print(r)
# print(l)
print(cnt)
