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: Accepted)

#include <stdio.h>

long p[100000];

int argmax(int l, int r){
  int nowmax=p[l];
  int maxindex=l;
  for(int i=l+1;i<=r;i++){
    if(p[i]>nowmax){
      maxindex=i;
      nowmax=p[i];
    }
  }
  return maxindex;
}

int ascending(int l, int r){
  for(int i=l;i<=r-1;i++){
    if(p[i]>p[i+1]) return 0;
  }
  return 1;
}

int descending(int l, int r){
  for(int i=l;i<=r-1;i++){
    if(p[i]<p[i+1]) return 0;
  }
  return 1;
}

long firstsum(int l, int r, int n){
  int i,imax;
  long ans;
  if(l==n && r==n) return 0;
  if(l!=n) imax=l;
  else imax=l+1;
  for(i=l+1;i<=r;i++){
    if(i!=n && p[i]>p[imax]) imax=i;
  }
  if(imax<n){
    ans=p[imax]*(imax-l+1)*(r-n+1)+firstsum(imax+1,r,n);
  }else{
    ans=p[imax]*(n-l+1)*(r-imax+1)+firstsum(l,imax-1,n);
  }
  return ans;
}

long secondsum(int l, int r){
  long ans=0;
  int imax,i,j;
  int ll[100000];
  int rr[100000];

  if(r-l<1) return 0;
  if(ascending(l,r)){
    for(i=l;i<=r-1;i++){
      ans+=p[i]*(i-l+1);
    }
    return ans;
  }
  if(descending(l,r)){
    for(i=r;i>=l+1;i--){
      ans+=p[i]*(r-i+1);
    }
    return ans;
  }
  imax=argmax(l,r);
  
  if(imax==l)
    ans=secondsum(imax+1,r)+firstsum(l,r,imax);
  else if(imax==r)
    ans=secondsum(l,imax-1)+firstsum(l,r,imax);
  else
    ans=secondsum(l,imax-1)+secondsum(imax+1,r)+firstsum(l,r,imax);
  return ans;
}

int main()
{
  int n;
  scanf("%d", &n);
  for(int i=0;i<n;i++) scanf("%d", &p[i]);
  printf("%ld\n",secondsum(0,n-1));  
  return 0;
}