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()))
p = [0]*(n+1)
ans = 0
for i in range(n):
  p[a[i]] = i+1
l = [i-1 for i in range(n+2)]
l[0] = 0
r = [i+1 for i in range(n+2)]
r[-1] = n+1
for i in range(n,0,-1):
  ans += (p[i]-l[p[i]])*(r[p[i]]-p[i])*i
  l[r[p[i]]] = l[p[i]]
  r[l[p[i]]] = r[p[i]]
print(ans)