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: Wrong Answer)

use std::cmp;

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 sorted(v: &[u64]) -> u64 {
    let mut b = true;
    for w in v.windows(2) {
        if w[0] > w[1] {
            b = false;
            break;
        }
    }
    if b {
        return (1..v.len()).map(|i| (i as u64) * v[i]).sum();
    }

    for w in v.windows(2) {
        if w[0] < w[1] {
            return 0;
        }
    }
    return (1..v.len()).map(|i| (i as u64) * v[v.len() - 1 - i]).sum();
}

fn evaluate(v: &[u64]) -> u64 {
    let n = v.len();
    if n == 0 {
        return 0;
    } else if n == 2 {
        return cmp::min(v[0], v[1]);
    } else if n == 3 {
        let a = cmp::min(v[0], v[1]);
        let b = cmp::min(v[1], v[2]);
        let mut v = vec![v[0], v[1], v[2]];
        v.sort();
        return a + b + v[1];
    }
    assert!(n != 1);

    let val = sorted(v);
    if val > 0 {
        return val;
    }

    let mid = n / 2;
    let edge = evaluate(&v[..mid]) + evaluate(&v[mid..]);

    let mut squre = 0;
    for i in 0..mid {
        let mut s: Vec<u64> = v[i..mid].iter().cloned().collect();
        s.sort();
        for &x in &v[mid..] {
            s.push(x);
            //s.sort();
            squre += s[s.len() - 2];
        }
    }

    edge + squre
}

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);
}