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)

from sys import stdin
import sys
import numpy as np
import collections
from functools import cmp_to_key
import heapq
sys.setrecursionlimit(100000)

##  input functions for me
def rsa(sep = ''):
    if sep == '' :
        return input().split() 
    else: return input().split(sep)
def rip(sep = ''):
    if sep == '' :
        return map(int, input().split()) 
    else: return map(int, input().split(sep))
def ria(sep = ''): 
    return list(rip(sep))
def ri(): return int(input())
def rd(): return float(input())
def rs(): return input()
##
def main():
    N = ri()
    P = [N+1,N+1] + ria() + [N+1,N+1]

    ord = []
    for i in range(2,N+2):
        ord.append((P[i], i))

    ord = sorted(ord) # P[i], i , P[i]順でソート

    # ..AsssBssCssDsssE.. のようになっている（Cが自分 A,B,D,E>C，s<C）
    # CからA,B,D,Eのインデクスを知りたいので，Cより小さい区間は連結にして置き，
    # スキップできるように各連結成分の両端に情報を乗せておく
    #  union-findで管理してもいいが，アクセスする場所と回数が限られているので配列で管理できる
    tot = 0
    l = [i for i in range(N + 4)]
    r = [i for i in range(N + 4)]
    used = [False] * (N + 4)
    for v, idx in ord:
        # 左右がusedならマージする
        used[idx] = True
        if used[idx - 1]:
            l[idx] = l[idx - 1]
            r[l[idx]] = idx
        if used[idx + 1]:
            r[idx] = r[idx + 1]
            l[r[idx]] = idx
        l0 = l[idx] - 1
        r0 = r[idx] + 1
        l1 = l0 - 1 if not used[l0 - 1] else (l[l0-1] - 1)
        r1 = r0 + 1 if not used[r0 + 1] else (r[r0+1] + 1)

        if l1 != 0:
            rseg = r0 - idx
            lseg = l0 - l1
            tot += lseg * rseg * v
        if r1 != N + 3:
            rseg = r1 - r0
            lseg = idx - l0
            tot += lseg * rseg * v

    print(tot)




if __name__ == "__main__":
    main()