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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

N = gets.to_i
P = gets.split.map(&:to_i)

def f(i)
  p = P[i]
  r1 = (i + 1 ... N).find{|j| P[j] > p} || N
  r2 = (r1 + 1... N).find{|j| P[j] > p} || N
  l1 = (i - 1).downto(0).find{|j| P[j] > p} || -1
  l2 = (l1 - 1).downto(0).find{|j| P[j] > p} || -1
  p*((l1 - l2)*(r1 - i) + (i - l1)*(r2 - r1))
end

puts (0 ... N).inject(0){|s, i| s + f(i)}