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: Runtime Error)

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()
}

fn evaluate(v: &[u64]) -> u64 {
    let n = v.len();
    let mut total = 0;
    let mut bs: Vec<Vec<[u64; 2]>> = Vec::new();
    let init = {
        let mut b = Vec::new();
        b.reserve(n);
        for w in v.windows(2) {
            let (max2, max) = if w[0] < w[1] {
                (w[0], w[1])
            } else {
                (w[1], w[0])
            };
            b.push([max2, max]);

            total += max2;
        }
        b
    };
    bs.push(init);

    for i in 0..(n - 2) {
        let mut maxes: Vec<[u64; 2]> = Vec::new();
        maxes.reserve(n);
        for w in bs[i].windows(2) {
            // a < b, c < d
            let (a, b, c, d) = (w[0][0], w[0][1], w[1][0], w[1][1]);
            let (max2, max) = {
                if b < d {
                    if b < c { (c, d) } else { (b, d) }
                } else if b > d {
                    if a < d { (d, b) } else { (a, b) }
                } else {
                    if a < c { (c, d) } else { (a, d) }
                }
            };
            maxes.push([max2, max]);

            total += max2;
        }
        bs.push(maxes);
    }
    total
}

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

    let ps_offset = (n * (n - 1) / 2) as u64;
    let val = evaluate(&ps);

    println!("{}", val + ps_offset);
}