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 Ruby (2.3.3) (judge verdict: Accepted)

# Try AtCoder
# author: Leonardone @ NEETSDKASU
############################################################
def gs() gets.strip end
def gi() gets.to_i end
def gf() gets.to_f end
def gss() gs.split end
def gis() gss.map(&:to_i) end
def nmapf(n,f) n.times.map{ __send__ f } end
def ngs(n) nmapf n,:gs end
def ngi(n) nmapf n,:gi end
def ngss(n) nmapf n,:gss end
def ngis(n) nmapf n,:gis end
def arr2d(h,w,v=0) h.times.map{[v] * w} end
def for2p(hr,wr,&pr) hr.each{|i|wr.each{|j| yield(i,j)}} end
def nsum(n) n * (n + 1) / 2 end
def vcount(d,r=Hash.new(0)) d.inject(r){|m,e| m[e]+=1;m} end
MV4 = [[0, 1], [1, 0], [0, -1], [-1, 0]]
MV8 = MV4 + [[1, 1], [1, -1], [-1, -1], [-1, 1]]
DV7 = 7 + 10 ** 9
############################################################
 
 

def f(s, sum)
    if s == ''
        sum
    else
        tmp = 0
        (1 .. s.length).each do |i|
            tmp += f(s[i .. -1], sum + s[0 ... i].to_i)
        end
        tmp
    end
end


p f(gs, 0)