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())
s=list(map(int,input().split()))
p,q,r,d=[0]*(n+1),[i for i in range(n+2)],[i for i in range(n+2)],0
for i in range(n):
    p[s[i]]=i
for i in range(n,0,-1):
    h=p[i]
    x,y=q[h],r[h]
    d+=i*(h-x+1)*(y-h+1)
    q[y+1],r[x-1]=x,y
print(d)