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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <stdio.h>

int main() {
  int N;
  int P[100001];
  int tmp=0;
  scanf("%d\n",&N);
  for (int i = 0; i < N; i++) {
    scanf("%d",&P[i]);
  }
//ここまで入力
  for (int i = 0; i < N-1; i++) {
    int M=0;
    int m=0;
    for (int j = i; j < N; j++) {
      if(P[j]>m){
        if (P[j]>M) {
          m = M;
          M = P[i];
        }else{
          m = P[i];
        }
      }
      tmp = tmp + m;
    }
  }
  printf("%d",tmp);
  return 0;
}