Problem:
Score : 900 points

Problem Statement

Takahashi has an empty string S and a variable x whose initial value is 0.

Also, we have a string T consisting of 0 and 1.

Now, Takahashi will do the operation with the following two steps |T| times.

Insert a 0 or a 1 at any position of S of his choice.

Then, increment x by the sum of the digits in the odd positions (first, third, fifth, ...) of S. For example, if S is 01101, the digits in the odd positions are 0, 1, 1 from left to right, so x is incremented by 2.

Print the maximum possible final value of x in a sequence of operations such that S equals T in the end.

Constraints

1 \leq |T| \leq 2 \times 10^5

T consists of 0 and 1.

Input

Input is given from Standard Input in the following format:

T

Output

Print the maximum possible final value of x in a sequence of operations such that S equals T in the end.

Sample Input 1

1101

Sample Output 1

5

Below is one sequence of operations that maximizes the final value of x to 5.

Insert a 1 at the beginning of S. S becomes 1, and x is incremented by 1.

Insert a 0 to the immediate right of the first character of S. S becomes 10, and x is incremented by 1.

Insert a 1 to the immediate right of the second character of S. S becomes 101, and x is incremented by 2.

Insert a 1 at the beginning of S. S becomes 1101, and x is incremented by 1.

Sample Input 2

0111101101

Sample Output 2

26

Solution in Rust (1.42.0) (judge verdict: Wrong Answer)

#[allow(dead_code)]
fn main() {
    let t = i::s();
    let mut zero = Vec::new();
    let mut one_count = 0;
    let mut zero_count = 0;
    let mut ans = 0usize;
    for c in t {
        match c {
            '0' => {
                zero_count += 1;
                zero.push((zero_count, one_count));
            }
            '1' => {
                one_count += 1;
            }
            _ => unreachable!(),
        }
    }
    let mut len = 0;
    for _ in 0..one_count {
        len += 1;
        ans += (len + 1) / 2;
    }

    zero.reverse();
    //  dbg!(&zero, &one_count, &zero_count);

    for &(zero_c, one_c) in &zero {
        //この0のあと、1が何個連続しているか
        let rest_one = one_count - one_c;

        let mut plus = 0;
        plus += (one_c + 1) / 2; //未処理の1
        if rest_one % 2 == 0 {
            plus += zero_c * (rest_one / 2);
        } else {
            plus += zero_c * ((rest_one - 1) / 2);
            if zero_c % 2 == 0 {
                plus += zero_c / 2;
            } else {
                //0が偶数番目に入るかどうかでカウント回数が変わる
                plus += zero_c / 2 + (one_count + 1) % 2;
            }
        }
        one_count = one_c;
        ans += plus;
        //  dbg!(&ans, &plus, &one_count, &one_c, &zero_c, &rest_one);
        //  println!();
    }

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

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::{HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::io::*;
#[allow(unused_imports)]
use std::num::*;
#[allow(unused_imports)]
use std::str::*;

#[allow(dead_code)]
mod i {
    use super::*;

    pub fn read<T: FromStr>() -> T {
        stdin()
            .bytes()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>()
            .parse::<T>()
            .ok()
            .unwrap()
    }
    pub fn str() -> String {
        read()
    }
    pub fn s() -> Vec<char> {
        str().chars().collect()
    }
    pub fn i() -> i64 {
        read()
    }
    pub fn u() -> usize {
        read()
    }
    pub fn u2() -> (usize, usize) {
        (read(), read())
    }
    pub fn u3() -> (usize, usize, usize) {
        (read(), read(), read())
    }
    pub fn u4() -> (usize, usize, usize, usize) {
        (read(), read(), read(), read())
    }
    pub fn u5() -> (usize, usize, usize, usize, usize) {
        (read(), read(), read(), read(), read())
    }
    pub fn u6() -> (usize, usize, usize, usize, usize, usize) {
        (read(), read(), read(), read(), read(), read())
    }
    pub fn f() -> f64 {
        read()
    }
    pub fn c() -> char {
        read::<String>().pop().unwrap()
    }
    pub fn iv(n: usize) -> Vec<i64> {
        (0..n).map(|_| i()).collect()
    }
    pub fn iv2(n: usize) -> Vec<(i64, i64)> {
        (0..n).map(|_| iv(2)).map(|a| (a[0], a[1])).collect()
    }
    pub fn iv3(n: usize) -> Vec<(i64, i64, i64)> {
        (0..n).map(|_| iv(3)).map(|a| (a[0], a[1], a[2])).collect()
    }
    pub fn uv(n: usize) -> Vec<usize> {
        (0..n).map(|_| u()).collect()
    }
    pub fn uv2(n: usize) -> Vec<(usize, usize)> {
        (0..n).map(|_| uv(2)).map(|a| (a[0], a[1])).collect()
    }
    pub fn uv3(n: usize) -> Vec<(usize, usize, usize)> {
        (0..n).map(|_| uv(3)).map(|a| (a[0], a[1], a[2])).collect()
    }
    pub fn uv4(n: usize) -> Vec<(usize, usize, usize, usize)> {
        (0..n)
            .map(|_| uv(4))
            .map(|a| (a[0], a[1], a[2], a[3]))
            .collect()
    }
    pub fn fv(n: usize) -> Vec<f64> {
        (0..n).map(|_| f()).collect()
    }
    pub fn cmap(h: usize) -> Vec<Vec<char>> {
        (0..h).map(|_| s()).collect()
    }
}