Problem:
Problem Statement

AtCoder currently hosts three types of contests: ABC, ARC, and AGC. As the number of users has grown, in order to meet the needs of more users, AtCoder has decided to increase the number of contests to 26 types, from AAC to AZC. For convenience, we number these 26 types as type 1 through type 26. AtCoder wants to schedule contests for D days so that user satisfaction is as high as possible. For every day, AtCoder will hold exactly one contest, and each contest will end on that day. The satisfaction is calculated as follows.

The satisfaction at the beginning of day 1 is 0. Satisfaction can be negative.

Holding contests increases satisfaction. The amount of increase will vary depending on a variety of factors. Specifically, we know in advance that holding a contest of type i on day d will increase the satisfaction by s_{d,i}.

If a particular type of contest is not held for a while, the satisfaction decreases. Each contest type i has an integer c_i, and at the end of each day d=1,2,...,D, the satisfaction decreases as follows. Let \mathrm{last}(d,i) be the last day before day d (including d) on which a contest of type i was held. If contests of type i have never been held yet, we define \mathrm{last}(d,i)=0. At the end of day d, the satisfaction decreases by \sum _{i=1}^{26}c_i \times (d-\mathrm{last}(d,i)).

Please schedule contests on behalf of AtCoder.
If the satisfaction at the end of day D is S, you will get a score of \max(10^6 + S, 0).
There are 50 test cases, and the score of a submission is the total scores for each test case.
You can make submissions multiple times, and the highest score among your submissions will be your score.

Constraints

D = 365

Each c_i is an integer satisfying 0\leq c_i \leq 100.

Each s_{d,i} is an integer satisfying 0\leq s_{d,i} \leq 20000.

Input

Input is given from Standard Input in the following format:

D
c_1 c_2 \cdots c_{26}
s_{1,1} s_{1,2} \cdots s_{1,26}
\vdots
s_{D,1} s_{D,2} \cdots s_{D,26}

Output

Let t_d (1\leq t_d \leq 26) be the type of the contest that will be held at day d.
Print D integers t_d to Standard Output in the following format:

t_1
t_2
\vdots
t_D

Any output that does not follow the above format may result in 0 pointsWA for that test case.

Input Generation

Each integer c_i and s_{d,i} is generated independently and uniformly at random from the integers in the range described in the problem statement.

Sample Input 1

5
86 90 69 51 2 96 71 47 88 34 45 46 89 34 31 38 97 84 41 80 14 4 50 83 7 82
19771 12979 18912 10432 10544 12928 13403 3047 10527 9740 8100 92 2856 14730 1396 15905 6534 4650 11469 3628 8433 2994 10899 16396 18355 11424
6674 17707 13855 16407 12232 2886 11908 1705 5000 1537 10440 10711 4917 10770 17272 15364 19277 18094 3929 3705 7169 6159 18683 15410 9092 4570
6878 4239 19925 1799 375 9563 3445 5658 19857 11401 6997 6498 19933 3848 2426 2146 19745 16880 17773 18359 3921 14172 16730 11157 5439 256
8633 15862 15303 10749 18499 7792 10317 5901 9395 11433 3514 3959 5202 19850 19469 9790 5653 784 18500 10552 17975 16615 7852 197 8471 7452
19855 17918 7990 10572 4333 438 9140 9104 12622 4985 12319 4028 19922 12132 16259 17476 2976 547 19195 19830 16285 4806 4471 9457 2864 2192

Sample Output 1

1
17
13
14
13

Note that this example is a small one for checking the problem specification. It does not satisfy the constraint D=365 and is never actually given as a test case. The final satisfaction with this output is 79325, so the score is 1079325.

Input generator, score calculator, and visualizer

Beginner's Guide

If you don't know what to do, proceed to problem B or C.

Solution in Common Lisp (SBCL 2.0.3) (judge verdict: Accepted)

(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 (ftype (function * (values fixnum &optional)) read-fixnum))
(defun read-fixnum (&optional (in *standard-input*))
  "NOTE: cannot read -2^62"
  (macrolet ((%read-byte ()
               `(the (unsigned-byte 8)
                     #+swank (char-code (read-char in nil #\Nul))
                     #-swank (sb-impl::ansi-stream-read-byte in nil #.(char-code #\Nul) nil))))
    (let* ((minus nil)
           (result (loop (let ((byte (%read-byte)))
                           (cond ((<= 48 byte 57)
                                  (return (- byte 48)))
                                 ((zerop byte) ; #\Nul
                                  (error "Read EOF or #\Nul."))
                                 ((= byte #.(char-code #\-))
                                  (setq minus t)))))))
      (declare ((integer 0 #.most-positive-fixnum) result))
      (loop
        (let* ((byte (%read-byte)))
          (if (<= 48 byte 57)
              (setq result (+ (- byte 48)
                              (* 10 (the (integer 0 #.(floor most-positive-fixnum 10))
                                         result))))
              (return (if minus (- result) result))))))))

(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
;;;

(declaim (inline calc-prob))
(defun calc-prob (prev-score new-score temp)
  (handler-bind ((floating-point-overflow (lambda (c) #>c (return-from calc-prob 1d0))))
    (exp (/ (- new-score prev-score) temp))))

(defun initialize-scores (d cs ss state)
  (declare (fixnum d)
           ((simple-array uint8 (*)) cs state)
           ((simple-array uint32 (* *)) ss))
  (let* ((prevs (make-array 26 :element-type 'int32 :initial-element -1))
         (res (make-array 26 :element-type 'int32 :initial-element 0)))
    (dotimes (i d)
      (let ((type (aref state i)))
        (incf (aref res type) (aref ss i type))
        (setf (aref prevs type) i)
        (dotimes (j 26)
          (decf (aref res j) (* (aref cs j) (- i (aref prevs j)))))))
    res))

(defun update-scores! (d cs ss state scores old-type new-type)
  (declare #.OPT
           (uint31 d)
           (fixnum old-type new-type)
           ((simple-array uint8 (*)) cs state)
           ((simple-array uint32 (365 26)) ss)
           ((simple-array int32 (*)) scores))
  (setf (aref scores old-type) 0
        (aref scores new-type) 0)
  (let* ((old-prev -1)
         (new-prev -1))
    (declare (int16 old-prev new-prev))
    (dotimes (i d)
      (let ((type (aref state i)))
        (cond ((= type old-type)
               (incf (aref scores type) (aref ss i type))
               (setq old-prev i)
               (decf (aref scores new-type) (* (aref cs new-type) (- i new-prev))))
              ((= type new-type)
               (incf (aref scores type) (aref ss i type))
               (setq new-prev i)
               (decf (aref scores old-type) (* (aref cs old-type) (- i old-prev))))
              (t (decf (aref scores old-type) (* (aref cs old-type) (- i old-prev)))
                 (decf (aref scores new-type) (* (aref cs new-type) (- i new-prev)))))))
    scores))

(defun solve (d cs ss init-state &optional (time 1.5d0))
  (declare #.OPT
           (double-float time)
           (uint32 d)
           ((simple-array uint8 (*)) cs init-state)
           ((simple-array uint32 (* *)) ss))
  (labels ((calc (scores) (loop for x across scores sum x of-type fixnum)))
    (let* ((state (copy-seq init-state))
           (scores (initialize-scores d cs ss state))
           (score (calc scores))
           (opt-scores (copy-seq scores))
           (opt-score (calc opt-scores))
           (opt-state (copy-seq state))
           (start-temp 1000d0)
           (end-temp 1d0)
           (loop-count 0))
      (declare (fixnum loop-count)
               (fixnum opt-score)
               ((simple-array int32 (*)) scores opt-scores)
               (double-float start-temp end-temp))
      (sb-int:with-progressive-timeout (rem-time :seconds time)
        (loop
          (incf loop-count)
          (let ((rem-time (float (rem-time) 1d0)))
            (when (zerop rem-time)
              (return))
            (let* ((day (random d))
                   (old-type (aref state day))
                   (new-type (random 26))
                   (old-score score))
              (unless (= old-type new-type)
                ;; tmp. update
                (setf (aref state day) new-type)
                (update-scores! d cs ss state scores old-type new-type)
                (let* ((new-score (calc scores))
                       (temp (+ end-temp (/ (* rem-time (- start-temp end-temp)) time)))
                       (prob (calc-prob old-score new-score temp)))
                  (declare (double-float temp))
                  ;; rollback
                  (when (> new-score opt-score)
                    (setq opt-scores (copy-seq scores)
                          opt-score new-score
                          opt-state (copy-seq state)))
                  (if (< (random 1.0) prob)
                      (setq score new-score)
                      (progn
                        (setf (aref state day) old-type)
                        (update-scores! d cs ss state scores new-type old-type)))))))))
      #>loop-count
      (assert (= opt-score (calc (initialize-scores d cs ss opt-state))))
      (values opt-state opt-scores))))

(defun print* (state)
  (write-string
   (with-output-to-string (*standard-output* nil :element-type 'base-char)
     (loop for x across state
           do (println (+ x 1))))))

(defun main ()
  (declare #.OPT)
  (let* ((d (read))
         (cs (make-array 26 :element-type 'uint8 :initial-element 0))
         (ss (make-array '(365 26) :element-type 'uint32 :initial-element 0)))
    (dotimes (i 26)
      (setf (aref cs i) (read-fixnum)))
    (dotimes (i d)
      (dotimes (j 26)
        (setf (aref ss i j) (read-fixnum))))
    ;; #>ss
    (let* ((prevs (make-array 26 :element-type 'int32 :initial-element -1))
           (init-state (make-array d :element-type 'uint8 :initial-element 0)))
      (dotimes (i (- d 2))
        (labels ((%eval (day type)
                   (let ((value (aref ss day type)))
                     (declare (fixnum value))
                     (dotimes (j 26)
                       (unless (= j type)
                         (decf value (* (aref cs j) (- day (aref prevs j))))))
                     value)))
          (let ((max-type1 0)
                (max-type2 0)
                (max-type3 0)
                (max-value most-negative-fixnum))
            (declare (fixnum max-value))
            (dotimes (type1 26)
              (let ((value1 (%eval i type1))
                    (store-i1 (aref prevs type1)))
                (setf (aref prevs type1) i)
                (dotimes (type2 26)
                  (let ((value2 (%eval (+ i 1) type2))
                        (store-i2 (aref prevs type2)))
                    (setf (aref prevs type2) (+ i 1))
                    (dotimes (type3 26)
                      (let ((value3 (%eval (+ i 2) type3)))
                        (when (> (+ value1 value2 value3) max-value)
                          (setq max-type1 type1
                                max-type2 type2
                                max-type3 type3
                                max-value (+ value1 value2 value3)))))
                    (setf (aref prevs type2) store-i2)))
                (setf (aref prevs type1) store-i1)))
            (setf (aref prevs max-type1) i
                  (aref init-state i) max-type1)
            (when (= i (- d 3))
              (setf (aref prevs max-type2) (+ i 1)
                    (aref init-state (+ i 1)) max-type2
                    (aref prevs max-type3) (+ i 2)
                    (aref init-state (+ i 2)) max-type3)))))
      (multiple-value-bind (state scores) (solve d cs ss init-state)
        (print* state)
        (loop for x across scores sum x)))))

#-swank (main)

;; (defun bench ()
;;   (let ((*random-state* (seed-random-state 0)))
;;     (loop repeat 5
;;           sum #>(run *dat-pathname*))))
;;;
;;; 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)
    (run-program "powershell.exe" '("-Command" "Get-Clipboard") :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 "365~%")
    (dotimes (i 26)
      (println (random 101) out))
    (dotimes (i 365)
      (dotimes (j 26)
        (println (random 20001) out)))))