Problem:
Score: 500 points

Problem Statement

Given is a permutation P of \{1, 2, \ldots, N\}.

For a pair (L, R) (1 \le L \lt R \le N), let X_{L, R} be the second largest value among P_L, P_{L+1}, \ldots, P_R.

Find \displaystyle \sum_{L=1}^{N-1} \sum_{R=L+1}^{N} X_{L,R}.

Constraints

2 \le N \le 10^5

1 \le P_i \le N

P_i \neq P_j (i \neq j)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
P_1 P_2 \ldots P_N

Output

Print \displaystyle \sum_{L=1}^{N-1} \sum_{R=L+1}^{N} X_{L,R}.

Sample Input 1

3
2 3 1

Sample Output 1

5

X_{1, 2} = 2, X_{1, 3} = 2, and X_{2, 3} = 1, so the sum is 2 + 2 + 1 = 5.

Sample Input 2

5
1 2 3 4 5

Sample Output 2

30

Sample Input 3

8
8 2 7 3 4 5 6 1

Sample Output 3

136

Solution in Python (3.4.3) (judge verdict: Runtime Error)

n=int(input())
p=list(map(int,input.split()))
s=[0,0]
t=[n+1,n+1]
a=[]
for i in reversed(range(1,n)):
  if p.index(i)<p.index(i+1):
    t.append(p.index(i+1))
  elif p.index(i)>p.index(i+1):
    s.append(p.index(i+1))
  w=sorted(s)[-1]
  x=sorted(s)[-2]
  y=sorted(t)[0]
  z=sorted(t)[1]
  c=(w-x)*(y-p.index(i))+(p.index(i)-w)*(z-y)
  a.append(i*c)
print(sum(a))