Problem:
Score : 300 points

Problem Statement

You are given a string S consisting of digits between 1 and 9, inclusive.
You can insert the letter + into some of the positions (possibly none) between two letters in this string.
Here, + must not occur consecutively after insertion.

All strings that can be obtained in this way can be evaluated as formulas.

Evaluate all possible formulas, and print the sum of the results.

Constraints

1 \leq |S| \leq 10

All letters in S are digits between 1 and 9, inclusive.

Input

The input is given from Standard Input in the following format:

S

Output

Print the sum of the evaluated value over all possible formulas.

Sample Input 1

125

Sample Output 1

176

There are 4 formulas that can be obtained: 125, 1+25, 12+5 and 1+2+5. When each formula is evaluated,

125

1+25=26

12+5=17

1+2+5=8

Thus, the sum is 125+26+17+8=176.

Sample Input 2

9999999999

Sample Output 2

12656242944

Solution in Rust (1.15.1) (judge verdict: Accepted)

#![allow(unused_imports)]
#![allow(dead_code)]
#![allow(unused_macros)]
#![allow(non_snake_case)]

use std::cmp::{max, min};
use std::cmp::Ordering::{self, Equal, Greater, Less};
use std::collections::{HashMap, HashSet};
use std::f64::consts::PI;
use std::io::Write;
use std::ops::{AddAssign, Sub};

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let 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")
    };
}

macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

trait Ext {
    type Item;

    fn lower_bound(&self, x: &Self::Item) -> usize
        where
            Self::Item: Ord;

    fn lower_bound_by<'a, F>(&'a self, f: F) -> usize
        where
            F: FnMut(&'a Self::Item) -> Ordering;

    fn lower_bound_by_key<'a, K, F>(&'a self, k: &K, f: F) -> usize
        where
            F: FnMut(&'a Self::Item) -> K,
            K: Ord;

    fn upper_bound(&self, x: &Self::Item) -> usize
        where
            Self::Item: Ord;

    fn upper_bound_by<'a, F>(&'a self, f: F) -> usize
        where
            F: FnMut(&'a Self::Item) -> Ordering;

    fn upper_bound_by_key<'a, K, F>(&'a self, k: &K, f: F) -> usize
        where
            F: FnMut(&'a Self::Item) -> K,
            K: Ord;

    fn equal_range(&self, x: &Self::Item) -> std::ops::Range<usize>
        where
            Self::Item: Ord;

    fn equal_range_by<'a, F>(&'a self, f: F) -> std::ops::Range<usize>
        where
            F: FnMut(&'a Self::Item) -> Ordering;

    fn equal_range_by_key<'a, K, F>(&'a self, k: &K, f: F) -> std::ops::Range<usize>
        where
            F: FnMut(&'a Self::Item) -> K,
            K: Ord;
}

impl<T> Ext for [T] {
    type Item = T;

    fn lower_bound(&self, x: &Self::Item) -> usize
        where
            T: Ord,
    {
        self.lower_bound_by(|y| y.cmp(x))
    }
    fn lower_bound_by<'a, F>(&'a self, mut f: F) -> usize
        where
            F: FnMut(&'a Self::Item) -> Ordering,
    {
        let s = self;
        let mut size = s.len();
        if size == 0 {
            return 0;
        }
        let mut base = 0usize;
        while size > 1 {
            let half = size / 2;
            let mid = base + half;
            let cmp = f(unsafe { s.get_unchecked(mid) });
            base = if cmp == Less { mid } else { base };
            size -= half;
        }
        let cmp = f(unsafe { s.get_unchecked(base) });
        base + (cmp == Less) as usize
    }
    fn lower_bound_by_key<'a, K, F>(&'a self, k: &K, mut f: F) -> usize
        where
            F: FnMut(&'a Self::Item) -> K,
            K: Ord,
    {
        self.lower_bound_by(|e| f(e).cmp(k))
    }

    fn upper_bound(&self, x: &Self::Item) -> usize
        where
            T: Ord,
    {
        self.upper_bound_by(|y| y.cmp(x))
    }

    fn upper_bound_by<'a, F>(&'a self, mut f: F) -> usize
        where
            F: FnMut(&'a Self::Item) -> Ordering,
    {
        let s = self;
        let mut size = s.len();
        if size == 0 {
            return 0;
        }
        let mut base = 0usize;
        while size > 1 {
            let half = size / 2;
            let mid = base + half;
            let cmp = f(unsafe { s.get_unchecked(mid) });
            base = if cmp == Greater { base } else { mid };
            size -= half;
        }
        let cmp = f(unsafe { s.get_unchecked(base) });
        base + (cmp != Greater) as usize
    }
    fn upper_bound_by_key<'a, K, F>(&'a self, k: &K, mut f: F) -> usize
        where
            F: FnMut(&'a Self::Item) -> K,
            K: Ord,
    {
        self.upper_bound_by(|e| f(e).cmp(k))
    }

    fn equal_range(&self, x: &Self::Item) -> std::ops::Range<usize>
        where
            T: Ord,
    {
        self.equal_range_by(|y| y.cmp(x))
    }
    fn equal_range_by<'a, F>(&'a self, mut f: F) -> std::ops::Range<usize>
        where
            F: FnMut(&'a Self::Item) -> Ordering,
    {
        let s = self;
        let mut size = s.len();
        if size == 0 {
            return 0..0;
        }
        let mut base = (0usize, 0usize);
        while size > 1 {
            let half = size / 2;
            let mid = (base.0 + half, base.1 + half);
            let cmp = (
                f(unsafe { s.get_unchecked(mid.0) }),
                f(unsafe { s.get_unchecked(mid.1) }),
            );
            base = (
                if cmp.0 == Less { mid.0 } else { base.0 },
                if cmp.1 == Greater { base.1 } else { mid.1 },
            );
            size -= half;
        }
        let cmp = (
            f(unsafe { s.get_unchecked(base.0) }),
            f(unsafe { s.get_unchecked(base.1) }),
        );
        (base.0 + (cmp.0 == Less) as usize..base.1 + (cmp.1 != Greater) as usize)
    }

    fn equal_range_by_key<'a, K, F>(&'a self, k: &K, mut f: F) -> std::ops::Range<usize>
        where
            F: FnMut(&'a Self::Item) -> K,
            K: Ord,
    {
        self.equal_range_by(|e| f(e).cmp(k))
    }
}

struct UnionFind {
    parts: Vec<usize>
}

impl UnionFind {
    fn new(n: usize) -> UnionFind {
        let parts = (0..n).collect();
        UnionFind { parts: parts }
    }

    fn union(&mut self, i: usize, j: usize) {
        let i_leader = self.find(i);
        let j_leader = self.find(j);
        self.parts[j_leader] = self.parts[i_leader];
    }

    fn find(&mut self, i: usize) -> usize {
        let mut p = i;
        while self.parts[p] != p {
            p = self.parts[p]
        };
        let mut s = i;
        while s != p {
            let t = self.parts[s];
            self.parts[s] = p;
            s = t
        };
        p
    }

    fn find_only(&self, i: usize) -> usize {
        let mut p = i;
        while self.parts[p] != p {
            p = self.parts[p]
        };
        p
    }

    fn same(&mut self, i: usize, j: usize) -> bool {
        self.find(i) == self.find(j)
    }

    fn same_only(&self, i: usize, j: usize) -> bool {
        self.find_only(i) == self.find_only(j)
    }
}

struct BinaryIndexTree<T> {
    data: Vec<T>,
}

impl<T> BinaryIndexTree<T>
    where
        T: Copy + AddAssign + Sub<Output=T> + Default,
{
    fn new(size: usize) -> Self {
        let buf_size = size.next_power_of_two();
        BinaryIndexTree {
            data: vec![T::default(); buf_size + 1],
        }
    }

    fn range_sum(&self, l: usize, r: usize) -> T {
        self.sum(r - 1) - self.sum(l - 1)
    }

    fn sum(&self, i: usize) -> T {
        let mut i = i as i64;
        let mut ret = T::default();
        while i > 0 {
            ret += self.data[i as usize];
            i -= i & -i;
        }
        ret
    }

    fn add(&mut self, i: usize, value: T) {
        assert!(i > 0);
        let n = self.data.len() as i64;
        let mut i = i as i64;
        while i <= n - 1 {
            self.data[i as usize] += value;
            i += i & -i;
        }
    }
}

#[inline]
fn clamp<T: PartialOrd>(input: T, min: T, max: T) -> T {
    debug_assert!(min <= max, "min must be less than or equal to max");
    if input < min {
        min
    } else if input > max {
        max
    } else {
        input
    }
}

#[inline]
fn coord_compress<T: std::clone::Clone + std::cmp::Ord>(src: Vec<T>) -> Vec<usize> {
    let mut tmp = src.clone();
    tmp.sort();
    tmp.dedup();
    src.iter()
        .map(|x| {
            tmp.binary_search(x).unwrap()
        })
        .collect()
}

#[inline]
fn binary_search<F>(l: i64, r: i64, query_fn: F) -> i64 where F: Fn(i64) -> bool {
    let mut size = r - l;
    let mut base = l;
    while size > 1 {
        let half = size / 2;
        let mid = base + half;
        if !query_fn(mid) {
            base = mid;
        }
        size -= half;
    }
    base + !query_fn(base) as i64
}

#[inline]
fn rel<T: PartialOrd + Default>(n: T) -> T {
    if n < T::default() {
        T::default()
    } else {
        n
    }
}

#[inline]
fn rem_euclid(a: i64, rhs: i64) -> i64 {
    let r = a % rhs;
    if r < 0 {
        if rhs < 0 {
            r - rhs
        } else {
            r + rhs
        }
    } else {
        r
    }
}

#[inline]
fn div_euclid(a: i64, rhs: i64) -> i64 {
    let q = a / rhs;
    if a % rhs < 0 {
        return if rhs > 0 { q - 1 } else { q + 1 };
    }
    q
}

fn main() {
    input! {
        aa: chars,
    }
    let aa: Vec<char> = aa;
    debug!(aa);

    let mut res = 0;
    for flags in 0..1 << aa.len() - 1 {
        let flags = flags | 1 << aa.len() - 1;

        let s = aa.iter()
            .enumerate()
            .scan(String::new(), |state, (idx, a)| {
                let mut y = state.clone();
                y.push(*a);

                if flags & (1 << idx) > 0 {
                    *state = String::new();
                    Some(y.parse::<usize>().unwrap())
                } else {
                    *state = y;
                    Some(0usize)
                }
            })
            .sum::<usize>();

        res += s;
    }

    println!("{:?}", res);
}