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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>

#define MAX_N 100001

int main(void){
  int i, j;

  int n;
  scanf("%d", &n);

  int max1, max2, temp;
  long sum=0;
  int p[n];
  int q[MAX_N]={};
  for(i=0; i<n; i++){
    scanf("%d", &p[i]);
    for(j=0; j<i; j++) q[j]++;
    if(i == 0) continue;
    max1=p[i], max2=0, temp=0;
    for(j=i-1; j>=0; j--){
      if(p[j] > max1){
        max2=max1;
        max1=p[j];
      }else if(p[j] > max2){
        max2=p[j];
      }
      sum += max2;
      if(q[p[i]] == 2){
        sum += (max2)*j;
        break;
      }
    }
  }

  printf("%ld\n", sum);
}