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=[int(j) for j in input().split()]
ans=0
l=list(range(n+2))
r=list(range(n+2))

index=[0]*(n+1)
for i in range(n):
    index[a[i]]=i

for i in range(1,n+1)[::-1]:
    ind=index[i]
    x,y=l[ind],r[ind]
    ans+=i*(ind-x+1)*(y-ind+1)
    l[y+1],r[x-1]=x,y
print(ans)




