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)

use std::collections::BTreeMap;
use std::collections::BTreeSet;

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let mut s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

fn main() {
    input!{
        n: usize,
        v: [usize; n],
    }

    let mut xlr = 0;
    let mut imap = BTreeMap::new();

    for i in 0..n {
        imap.insert(v[i], i);
    }

    let mut iter = imap.iter().rev();

    let mut iset = BTreeSet::new();
    iset.insert(0);
    iset.insert(n+1);

    for (key, value) in iter {

        iset.insert((*value)+1);
        let mut sset = iset.split_off(&(value+1));
        //let mut trange = iset.range(0..value+1).rev();
        let mut x = 0;
        let mut w = 0;
        {
            let mut trange = iset.iter().rev();
            x = *trange.next().unwrap();
            if x != 0 {
                w = *trange.next().unwrap(); 
            }
        } 

        //let mut srange = iset.range(value+1..n+2);
        let mut y = 0;
        let mut z = (n+1);
        {
            let mut srange = sset.iter();
            srange.next();
            y = *srange.next().unwrap();
            if y != (n+1) {
                z = *srange.next().unwrap();
            }
        }

        xlr = xlr + ((x - w) * (y - (value+1)) + ((value+1) - x) * (z - y)) * key;

        for sn in sset.iter() {
            iset.insert(*sn);
        }

        if key == &0 {
            break;
        }

    }

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