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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	public void Solve(){
		int[] ord = new int[N];
		for(int i=0;i<N;i++) ord[i] = i;
		Array.Sort(ord, (i,j) => -1 * (A[i].CompareTo(A[j])));
		//Console.WriteLine("ord:{0}",String.Join(" ",ord));
		var sl = new SortedList<int,int>();
		sl.Add(-2,-2);
		sl.Add(-1,-1);
		sl.Add(N,N);
		sl.Add(N+1,N+1);
		long tot = 0;
		for(int i=0;i<N;i++){
			int k = ord[i];
			long v = A[k];
			sl.Add(k,k);
			var idx = sl.IndexOfKey(k);
			var l1 = sl.Keys[idx - 2];
			var l0 = sl.Keys[idx - 1];
			var r0 = sl.Keys[idx + 1];
			var r1 = sl.Keys[idx + 2];
			// #...#...x...#...#
			//  L......RRRR.....
			//     L...RRRR.....
			//      L......RRRR.
			//         L...RRRR.
			//Console.WriteLine("{0} {1} {2} {3} {4}",l1,l0,k,r0,r1);
			if(l1 != -2){
				long rs = r0 - k;
				long ls = l0 - l1;
				tot += rs * ls * v;
			}
			if(r1 != N + 1){
				long rs = r1 - r0;
				long ls = k - l0;
				tot += rs * ls * v;
			}
		}
		Console.WriteLine(tot);


	}
	int N;
	long[] A;
	public Sol(){
		N = ri();
		A = rla();		
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}