Problem:
Score : 400 points

Problem Statement

We have a grid with H rows and W columns. At first, all cells were painted white.

Snuke painted N of these cells. The i-th ( 1 \leq i \leq N ) cell he painted is the cell at the a_i-th row and b_i-th column.

Compute the following:

For each integer j ( 0 \leq j \leq 9 ), how many subrectangles of size 3×3 of the grid contains exactly j black cells, after Snuke painted N cells?

Constraints

3 \leq H \leq 10^9

3 \leq W \leq 10^9

0 \leq N \leq min(10^5,H×W)

1 \leq a_i \leq H (1 \leq i \leq N)

1 \leq b_i \leq W (1 \leq i \leq N)

(a_i, b_i) \neq (a_j, b_j) (i \neq j)

Input

The input is given from Standard Input in the following format:

H W N
a_1 b_1
:
a_N b_N

Output

Print 10 lines.
The (j+1)-th ( 0 \leq j \leq 9 ) line should contain the number of the subrectangles of size 3×3 of the grid that contains exactly j black cells.

Sample Input 1

4 5 8
1 1
1 4
1 5
2 3
3 1
3 2
3 4
4 4

Sample Output 1

0
0
0
2
4
0
0
0
0
0

There are six subrectangles of size 3×3. Two of them contain three black cells each, and the remaining four contain four black cells each.

Sample Input 2

10 10 20
1 1
1 4
1 9
2 5
3 10
4 2
4 7
5 9
6 4
6 6
6 7
7 1
7 3
7 7
8 1
8 5
8 10
9 2
10 4
10 9

Sample Output 2

4
26
22
10
2
0
0
0
0
0

Sample Input 3

1000000000 1000000000 0

Sample Output 3

999999996000000004
0
0
0
0
0
0
0
0
0

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

;; -*- coding: utf-8 -*-
(eval-when (:compile-toplevel :load-toplevel :execute)
  (defparameter OPT
    #+swank '(optimize (speed 3) (safety 2))
    #-swank '(optimize (speed 3) (safety 0) (debug 0)))
  #+swank (ql:quickload '(:cl-debug-print :fiveam))
  #-swank (set-dispatch-macro-character #\# #\> (lambda (s c p) (declare (ignore c p)) (read s nil (values) 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*))
  (declare #.OPT)
  (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 #\-))
                                  (setf 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))))))))

(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

(defmacro dx (form)
  (let ((tmp (gensym)))
    `(let ((,tmp ,form))
       (declare (dynamic-extent ,tmp))
       ,tmp)))

(defun main ()
  (declare #.OPT)
  (let* ((h (read))
         (w (read))
         (n (read))
         (table (make-hash-table :test #'equal :size n))
         (res (make-array 10 :element-type 'uint32 :initial-element 0)))
    (declare (uint31 h w n))
    (dotimes (i n)
      (let ((a (- (read-fixnum) 1))
            (b (- (read-fixnum) 1)))
        (declare (uint32 a b))
        (setf (gethash (cons a b) table) t)))
    (labels ((frob (y x)
               (declare (int32 y x))
               (if (or (< y 0) (< x 0))
                   0
                   (let ((res 0)
                         (pair (cons 0 0)))
                     (declare (uint32 res)
                              ((cons fixnum fixnum) pair)
                              (sb-impl::truly-dynamic-extent pair))
                     (setf (car pair) y (cdr pair) x)
                     (when (gethash pair table) (incf res))
                     (setf (car pair) (+ y 1) (cdr pair) x)
                     (when (gethash pair table) (incf res))
                     (setf (car pair) (+ y 2) (cdr pair) x)
                     (when (gethash pair table) (incf res))
                     (setf (car pair) y (cdr pair) (+ x 1))
                     (when (gethash pair table) (incf res))
                     (setf (car pair) (+ y 1) (cdr pair) (+ x 1))
                     (when (gethash pair table) (incf res))
                     (setf (car pair) (+ y 2) (cdr pair) (+ x 1))
                     (when (gethash pair table) (incf res))
                     (setf (car pair) y (cdr pair) (+ x 2))
                     (when (gethash pair table) (incf res))
                     (setf (car pair) (+ y 1) (cdr pair) (+ x 2))
                     (when (gethash pair table) (incf res))
                     (setf (car pair) (+ y 2) (cdr pair) (+ x 2))
                     (when (gethash pair table) (incf res))
                     res))))
      (loop for (y . x) of-type (uint32 . uint32) being each hash-key of table
            do (when (< (+ y 2) h)
                 (when (< (+ x 2) w)
                   (incf (aref res (frob y x))))
                 (when (< (+ x 1) w)
                   (incf (aref res (frob y (- x 1)))))
                 (incf (aref res (frob y (- x 2)))))
               (when (< (+ y 1) h)
                 (when (< (+ x 2) w)
                   (incf (aref res (frob (- y 1) x))))
                 (when (< (+ x 1) w)
                   (incf (aref res (frob (- y 1) (- x 1)))))
                 (incf (aref res (frob (- y 1) (- x 2)))))
               (when (< (+ x 2) w)
                 (incf (aref res (frob (- y 2) x))))
               (when (< (+ x 1) w)
                 (incf (aref res (frob (- y 2) (- x 1)))))
               (incf (aref res (frob (- y 2) (- x 2)))))
      (loop for i from 1 to 9
            do (setf (aref res i) (/ (aref res i) i)))
      (println (- (* (- h 2) (- w 2))
                  (reduce #'+ res :start 1)))
      (loop for i from 1 to 9
            do (println (aref res i))))))

#-swank (main)