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