(eval-when (:compile-toplevel :load-toplevel :execute)
  (sb-int:defconstant-eqx opt
    #+swank '(optimize (speed 3) (safety 2))
    #-swank '(optimize (speed 3) (safety 0) (debug 0))
    #'equal)
  #+swank (ql:quickload '(:cl-debug-print :fiveam) :silent t)
  #-swank (set-dispatch-macro-character
           #\# #\> (lambda (s c p) (declare (ignore c p)) `(values ,(read s nil nil t)))))
#+swank (cl-syntax:use-syntax cl-debug-print:debug-print-syntax)
#-swank (disable-debugger) ; for CS Academy

;; BEGIN_INSERTED_CONTENTS
(declaim (inline make-mod-power-table))
(defun make-mod-power-table (base length modulus &optional (element-type '(unsigned-byte 31)))
  "Returns a vector of the given length: VECTOR[x] := BASE^x mod MODULUS."
  (declare (fixnum base)
           ((integer 0 #.most-positive-fixnum) length)
           ((integer 1 #.most-positive-fixnum) modulus))
  (let ((res (make-array length :element-type element-type)))
    (unless (zerop length)
      (setf (aref res 0) 1)
      (loop for i from 1 below length
            do (setf (aref res i)
                     (mod (* base (aref res (- i 1))) modulus))))
    res))

(in-package :cl-user)

(defmacro dbg (&rest forms)
  #+swank
  (if (= (length forms) 1)
      `(format *error-output* "~A => ~A~%" ',(car forms) ,(car forms))
      `(format *error-output* "~A => ~A~%" ',forms `(,,@forms)))
  #-swank (declare (ignore forms)))

(defmacro define-int-types (&rest bits)
  `(progn
     ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "UINT~A" b)) () '(unsigned-byte ,b))) bits)
     ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "INT~A" b)) () '(signed-byte ,b))) bits)))
(define-int-types 2 4 7 8 15 16 31 32 62 63 64)

(declaim (inline println))
(defun println (obj &optional (stream *standard-output*))
  (let ((*read-default-float-format* 'double-float))
    (prog1 (princ obj stream) (terpri stream))))

(defconstant +mod+ 1000000007)

;;;
;;; Body
;;;

(defun calc (num)
  (declare (uint62 num))
  (loop for i from 0
        when (zerop num)
        do (return i)
        do (setq num (mod num (logcount num)))))

(defun main ()
  (declare #.opt)
  (let* ((n (read))
         (string-xs (read-line))
         (xs (map 'simple-bit-vector #'digit-char-p string-xs))
         (c (count 1 xs))
         (powers+ (make-mod-power-table 2 n (+ c 1)))
         (powers- (make-mod-power-table 2 n (max 1 (- c 1))))
         (x+ 0)
         (x- 0))
    (declare ((simple-array uint31 (*)) powers+ powers-)
             (uint31 c x+ x-))
    (let ((xs (reverse xs)))
      (dotimes (i n)
        (when (= 1 (aref xs i))
          (setq x+ (mod (+ (aref powers+ i) x+) (+ c 1)))))
      (when (>= c 2)
        (dotimes (i n)
          (when (= 1 (aref xs i))
            (setq x- (mod (+ (aref powers- i) x-) (- c 1)))))))
    (write-string
     (with-output-to-string (*standard-output* nil :element-type 'base-char)
       (dotimes (i n)
         (println
          (if (zerop (aref xs i))
              (let ((init (mod (+ x+ (aref powers+ (- n i 1))) (+ c 1))))
                (+ 1 (calc init)))
              (if (= c 1)
                  0
                  (let ((init (mod (- x- (aref powers- (- n i 1))) (- c 1))))
                    (+ 1 (calc init)))))))))))

#-swank (main)

;;;
;;; Test and benchmark
;;;

#+swank
(defun io-equal (in-string out-string &key (function #'main) (test #'equal))
  "Passes IN-STRING to *STANDARD-INPUT*, executes FUNCTION, and returns true if
the string output to *STANDARD-OUTPUT* is equal to OUT-STRING."
  (labels ((ensure-last-lf (s)
             (if (eql (uiop:last-char s) #\Linefeed)
                 s
                 (uiop:strcat s uiop:+lf+))))
    (funcall test
             (ensure-last-lf out-string)
             (with-output-to-string (out)
               (let ((*standard-output* out))
                 (with-input-from-string (*standard-input* (ensure-last-lf in-string))
                   (funcall function)))))))

#+swank
(defun get-clipbrd ()
  (with-output-to-string (out)
    #+os-windows (run-program "powershell.exe" '("-Command" "Get-Clipboard") :output out :search t)
    #+os-unix (run-program "xsel" '("-b" "-o") :output out :search t)))

#+swank (defparameter *this-pathname* (uiop:current-lisp-file-pathname))
#+swank (defparameter *dat-pathname* (uiop:merge-pathnames* "test.dat" *this-pathname*))

#+swank
(defun run (&optional thing (out *standard-output*))
  "THING := null | string | symbol | pathname

null: run #'MAIN using the text on clipboard as input.
string: run #'MAIN using the string as input.
symbol: alias of FIVEAM:RUN!.
pathname: run #'MAIN using the text file as input."
  (let ((*standard-output* out))
    (etypecase thing
      (null
       (with-input-from-string (*standard-input* (delete #\Return (get-clipbrd)))
         (main)))
      (string
       (with-input-from-string (*standard-input* (delete #\Return thing))
         (main)))
      (symbol (5am:run! thing))
      (pathname
       (with-open-file (*standard-input* thing)
         (main))))))

#+swank
(defun gen-dat ()
  (uiop:with-output-file (out *dat-pathname* :if-exists :supersede)
    (format out "200000~%")
    (dotimes (i 200000 (terpri out))
      (write (random 2) :stream out))))

#+swank
(defun bench (&optional (out (make-broadcast-stream)))
  (time (run *dat-pathname* out)))

;; To run: (5am:run! :sample)
#+swank
(it.bese.fiveam:test :sample
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "3
011
"
    "2
1
1
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "23
00110111001011011001110
"
    "2
1
2
2
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
3
")))


Measured memory_bytes: 30176