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: Time Limit Exceeded)

import bisect

N = int(input())
P = list(enumerate(list(map(int, input().split()))))
P = sorted(P, key=lambda x:x[1], reverse=True)

ans = 0
larger_indexes = [-1, -1, N, N]
for i, p in P:
  idx = bisect.bisect_left(larger_indexes, i)
  ir1, ir2 = larger_indexes[idx], larger_indexes[idx+1]
  il1, il2 = larger_indexes[idx-1], larger_indexes[idx-2]
  ans += ((ir1-i)*(il1-il2) + (ir2-ir1)*(i-il1)) * p
  bisect.insort(larger_indexes, i)

print(ans)