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 python3
ans=0
n=int(input())
A=list(map(int,input().split()))
B=[0]*(n+1)
for i in range(n):
    B[A[i]]=i+1
LL=[int(i) for i in range(n+2)]
RR=[int(i) for i in range(n+2)]
for i in range(n,0,-1):
    l=LL[B[i]]
    r=RR[B[i]]
    ans+=(B[i]-l+1)*(r-B[i]+1)*i
    LL[r+1]=l
    RR[l-1]=r
print(ans)
