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 Common Lisp (SBCL 1.1.14) (judge verdict: Wrong Answer)

(defun bit-full-serarch (n)
  (let ((result nil))
    (do ((bit 0 (1+ bit)))
        ((> bit (ash 1 n)))
      (let ((tmp nil))
        (do ((i 0 (1+ i)))
            ((> i n))
          (when (/= 0 (logand  bit (ash 1 i)))
            (push i tmp)))
        (when tmp
          (push tmp result))
        ))
    result))

(defmacro char-list-to-string-to-number (l)
  `(parse-integer (coerce ,l 'string)))

(defun calc (target pos-list &optional (count 0) tmp result)
  (cond ((null target)
         (when tmp
           (let ((tmp-l (char-list-to-string-to-number (reverse tmp))))
             (if (null (listp tmp-l))
                 (push tmp-l result)
                 (push (reduce #'+ tmp-l) result))))
         (reverse result))
        ((and pos-list (= count (car pos-list)))
         (let ((tmp-l (char-list-to-string-to-number (reverse tmp))))
           (if (null (listp tmp-l))
               (push tmp-l result)
               (push (reduce #'+ tmp-l) result))
           (setq tmp nil))
         (push (car target) tmp)
         (calc (cdr target) (cdr pos-list) (- count 1) tmp result))
        (t
         (push (car target) tmp)
         (calc (cdr target) pos-list (- count 1) tmp result))))

(defun main ()
  (let* ((target (coerce (read-line) 'list))
         (pos-list (bit-full-serarch (- (length target) 1)))
         (result 0)
         (size (- (length target) 1)))
    ;; (print pos-list)
    (dolist (x pos-list)
      (if (= size (car x))
          (let ((tmp (parse-integer (coerce target 'string))))
            (setq result (+ result tmp)))
          (let ((tmp (calc target x (- (length target) 1))))
            ;; (format t "~%~A: ~A~%~%" x tmp)
            (setq result (+ result (reduce #'+ tmp)))
            )))
    (princ result)))