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(i) for i in input().split()]

def f(A):
  P=[0]*N
  S=[(-1,0)]
  for i,b in enumerate(A):
    while S[-1][1]>b:
      S.pop()
    P[b-1]=i-S[-1][0]
    S.append((i,b))
  return P
P=f(a)
Q=f(a[::-1])
ans=0
for i in range(N):
  ans+=(i+1)*P[i]*Q[i]
print(ans)
  
  
  