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 sys
sys.setrecursionlimit(10**7)

n=int(input())
b=input().split()
for i in range(n):
    b[i]=int(b[i])

def main(l,m1,m2,c,s):
    c+=1
    #print(m1,m2,s,c)
    while c<n-l:
        if c==1:
            m1=max(b[l],b[l+1])
            m2=min(b[l],b[l+1])
            s+=m2
            c+=1
            #print(m1,m2,s,c)
        elif b[l+c]>m1:
            m2=m1
            m1=b[l+c]
            s+=m2
            c+=1
        elif b[l+c]>m2:
            m2=b[l+c]
            s+=m2
            c+=1
        else:
            s+=m2
            c+=1
    return s
s1=0
for i in range(n-1):
    s=main(i,0,0,0,0)
    #print(s)
    s1+=s
    #print(s,s1)
print(s1)