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: Wrong Answer)

n=int(input())
p=list(map(int,input().split()))

index=[0]
for i in range(1,n+1):
  index.append(p.index(i)+1)

s=[0,0,index[n],n+1,n+1]
a=[]

import bisect
for i in reversed(range(1,n)):
  bisect.insort_left(s,index[i])
  t=s.index(index[i])
  
  w=s[t-2]
  x=s[t-1]
  y=s[t+1]
  z=s[t+2]
  c=(x-w)*(y-index[i])+(index[i]-x)*(z-y)
  a.append(i*c)

print(sum(a))
print(s)