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 Rust (1.15.1) (judge verdict: Time Limit Exceeded)

fn read_line() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim_right().to_owned()
}

fn to_vec(s: String, offset: u64) -> Vec<u64> {
    s.split_whitespace()
        .map(|s| s.parse::<u64>().unwrap() - offset)
        .collect()
}

trait Container {
    fn last2(&self) -> u64;
}

impl Container for Vec<u64> {
    fn last2(&self) -> u64 {
        if self.len() < 2 {
            return 0;
        }
        self[self.len() - 2]
    }
}

fn main() {
    let n: usize = read_line().parse().unwrap();
    let ps = to_vec(read_line(), 1);

    let mut v: Vec<Vec<Vec<u64>>> = vec![vec![Vec::new(); n]; n];

    let mut map = vec![0; n];
    for (i, &p) in ps.iter().enumerate() {
        map[p as usize] = i;
    }

    for p_i in 0..n {
        let p = map[p_i];
        for i in p..n {
            for j in 0..(p + 1) {
                v[i][j].push(p_i as u64);
            }
        }
    }

    let mut total = (n * (n - 1) / 2) as u64;
    for vv in v {
        for vvv in vv {
            total += vvv.last2();
        }
    }

    println!("{}", total);
}