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)

S = gets.chomp.split("")
$debug = false

### DFS: Depth-First Search = 深さ優先探索
# スタックによる実装
def iterative_dfs(patterns, limit)
  # スタックとなる配列を用意し、初期状態である空文字列を格納する
  stack = [""]
  until stack.empty?
    # スタックから1つ取り出す（末尾から取り出すのでpopを使う）
    string = stack.pop

    if string.length == limit
      # 頂点に達した際、文字列を配列に格納する
      patterns << string.split("").to_a.unshift(nil) unless string.empty?
    else
      # 分岐処理
      stack << string + " "
      stack << string + "+"
    end
  end
end

patterns = [] # 結果を格納する配列を用意しておく
iterative_dfs(patterns, S.size - 1)
p patterns if $debug # 組み合わせの表示

answer = 0
patterns.each do |pattern|
  expression = S[0]
  (1...S.length).each do |i|
    expression += "+" if pattern[i] == "+"
    expression += S[i]
  end
  p expression if $debug
  p eval expression if $debug
  answer += eval expression
end

# 入力が1桁の場合の考慮を忘れていた……。
if S.size == 1
  answer = S[0].to_i
end

puts answer