Problem p04000 (python)

Fixed submission:
#!/usr/bin/env python3

import sys
# import math
# from string import ascii_lowercase, ascii_uppercase, ascii_letters, digits, hexdigits
# import re                                    # re.compile(pattern) => ptn obj; p.search(s), p.match(s), p.finditer(s) => match obj; p.sub(after, s)
# from operator import itemgetter              # itemgetter(1), itemgetter('key')
# from collections import deque                # deque class. deque(L): dq.append(x), dq.appendleft(x), dq.pop(), dq.popleft(), dq.rotate()
# from collections import defaultdict          # subclass of dict. defaultdict(facroty)
# from collections import Counter              # subclass of dict. Counter(iter): c.elements(), c.most_common(n), c.subtract(iter)
# from heapq import heapify, heappush, heappop # built-in list. heapify(L) changes list in-place to min-heap in O(n), heappush(heapL, x) and heappop(heapL) in O(lgn).
# from heapq import nlargest, nsmallest        # nlargest(n, iter[, key]) returns k-largest-list in O(n+klgn).
# from itertools import count, cycle, repeat   # count(start[,step]), cycle(iter), repeat(elm[,n])
# from itertools import groupby                # [(k, list(g)) for k, g in groupby('000112')] returns [('0',['0','0','0']), ('1',['1','1']), ('2',['2'])]
# from itertools import starmap                # starmap(pow, [[2,5], [3,2]]) returns [32, 9]
# from itertools import product, permutations  # product(iter, repeat=n), permutations(iter[,r])
# from itertools import combinations, combinations_with_replacement
# from itertools import accumulate             # accumulate(iter[, f])
# from functools import reduce                 # reduce(f, iter[, init])
# from functools import lru_cache              # @lrucache ...arguments of functions should be able to be keys of dict (e.g. list is not allowed)
# from bisect import bisect_left, bisect_right # bisect_left(a, x, lo=0, hi=len(a)) returns i such that all(val<x for val in a[lo:i]) and all(val>-=x for val in a[i:hi]).
# from copy import deepcopy                    # to copy multi-dimentional matrix without reference
# from fractions import gcd                    # for Python 3.4 (previous contest @AtCoder)


def main():
    mod = 1000000007                # 10^9+7
    inf = float('inf')              # sys.float_info.max = 1.79...e+308
    # inf = 2 ** 64 - 1               # (for fast JIT compile in PyPy) 1.84...e+19
    sys.setrecursionlimit(10**6)    # 1000 -> 1000000
    def input(): return sys.stdin.readline().rstrip()
    def ii():    return int(input())
    def mi():    return map(int, input().split())
    def mi_0():  return map(lambda x: int(x)-1, input().split())
    def lmi():   return list(map(int, input().split()))
    def lmi_0(): return list(map(lambda x: int(x)-1, input().split()))
    def li():    return list(input())


    def contained_in_dict_set(d, i, j):
        if i in d:
            if j in d[i]:
                return True
        return False
    
    def register_dict_set(d, i, j):
        if i not in d:
            d[i] = set()
        d[i].add(j)

    def count_black_around_center(point_dict, i, j):
        cnt = 0
        for s in range(i-1, i+2):
            for t in range(j-1, j+2):
                if contained_in_dict_set(point_dict, s, t):
                    cnt += 1
        return cnt
    

    h, w, n = mi()
    points = [lmi() for _ in range(n)]
    num_of_grids_contains_black = [0] * 10

    point_dict = dict()
    visited_dict = dict()

    for x, y in points:
        register_dict_set(point_dict, x, y)

    for x, y in points:
        for i in range(x-1, x+2):
            for j in range(y-1, y+2):
                if 2<=i<=h-1 and 2<=j<=w-1 and not contained_in_dict_set(visited_dict, i, j):
                    cnt = count_black_around_center(point_dict, i, j)
                    num_of_grids_contains_black[cnt] += 1
                    register_dict_set(visited_dict, i, j)
    
    num_of_grids_contains_black[0] = (h - 2) * (w - 2) - sum(num_of_grids_contains_black[1:])
    print(*num_of_grids_contains_black, sep='\n')    



if __name__ == "__main__":
    main()

Buggy submission (verdict: Runtime Error):
#!/usr/bin/env python3

import sys
# import math
# from string import ascii_lowercase, ascii_uppercase, ascii_letters, digits, hexdigits
# import re                                    # re.compile(pattern) => ptn obj; p.search(s), p.match(s), p.finditer(s) => match obj; p.sub(after, s)
from operator import itemgetter              # itemgetter(1), itemgetter('key')
# from collections import deque                # deque class. deque(L): dq.append(x), dq.appendleft(x), dq.pop(), dq.popleft(), dq.rotate()
# from collections import defaultdict          # subclass of dict. defaultdict(facroty)
# from collections import Counter              # subclass of dict. Counter(iter): c.elements(), c.most_common(n), c.subtract(iter)
# from heapq import heapify, heappush, heappop # built-in list. heapify(L) changes list in-place to min-heap in O(n), heappush(heapL, x) and heappop(heapL) in O(lgn).
# from heapq import nlargest, nsmallest        # nlargest(n, iter[, key]) returns k-largest-list in O(n+klgn).
# from itertools import count, cycle, repeat   # count(start[,step]), cycle(iter), repeat(elm[,n])
# from itertools import groupby                # [(k, list(g)) for k, g in groupby('000112')] returns [('0',['0','0','0']), ('1',['1','1']), ('2',['2'])]
# from itertools import starmap                # starmap(pow, [[2,5], [3,2]]) returns [32, 9]
# from itertools import product, permutations  # product(iter, repeat=n), permutations(iter[,r])
# from itertools import combinations, combinations_with_replacement
# from itertools import accumulate             # accumulate(iter[, f])
# from functools import reduce                 # reduce(f, iter[, init])
# from functools import lru_cache              # @lrucache ...arguments of functions should be able to be keys of dict (e.g. list is not allowed)
# from bisect import bisect_left, bisect_right # bisect_left(a, x, lo=0, hi=len(a)) returns i such that all(val<x for val in a[lo:i]) and all(val>-=x for val in a[i:hi]).
# from copy import deepcopy                    # to copy multi-dimentional matrix without reference
# from fractions import gcd                    # for Python 3.4 (previous contest @AtCoder)
from random import shuffle

def main():
    mod = 1000000007                # 10^9+7
    inf = float('inf')              # sys.float_info.max = 1.79...e+308
    # inf = 2 ** 64 - 1               # (for fast JIT compile in PyPy) 1.84...e+19
    sys.setrecursionlimit(10**6)    # 1000 -> 1000000
    def input(): return sys.stdin.readline().rstrip()
    def ii():    return int(input())
    def mi():    return map(int, input().split())
    def mi_0():  return map(lambda x: int(x)-1, input().split())
    def lmi():   return list(map(int, input().split()))
    def lmi_0(): return list(map(lambda x: int(x)-1, input().split()))
    def li():    return list(input())
    

    class TwoDimNode:
        def __init__(self, x=None, y=None, parent=None, left=None, right=None):
            """
            2 次元二分探索木のためのノード
            """        
            self.x = x
            self.y = y
            self.parent = parent
            self.left = left
            self.right = right
            self.flag = True

    class TwoDimTree:
        def __init__(self, points=[]):
            """
            2 次元二分探索木 (kD tree) を作成する
            root の深さを 0 として、深さが偶数の場合そこでは x を基準に、奇数の場合 y を基準に二分探索木条件を満たすようにする
            """
            # nil の設定
            self.nil = TwoDimNode()
            self.nil.parent = self.nil
            self.nil.left = self.nil
            self.nil.right = self.nil
            # root の設定
            self.root = self.nil
            # もし予め一次元の点の集合が与えられるのならバランスする形で kD tree を構築する
            self._balance_insert(points)
        
        def preorder_traverse(self, node=None):
            node = self.root if node is None else node
            if node != self.nil:
                print(f"({node.x},{node.y})", end=' ')
                self.preorder_traverse(node=node.left)
                self.preorder_traverse(node=node.right)
            
        def postorder_traverse(self, node=None):
            node = self.root if node is None else node
            if node != self.nil:
                self.preorder_traverse(node=node.left)
                self.preorder_traverse(node=node.right)
                print(f"({node.x},{node.y})", end=' ')

        def inorder_traverse(self, node=None):
            node = self.root if node is None else node
            if node != self.nil:
                self.preorder_traverse(node=node.left)
                print(f"({node.x},{node.y})", end=' ')
                self.preorder_traverse(node=node.right)
        
        def _balance_insert(self, seq, depth=0):
            # 毎回 x or y をキーとしてソートを行い、中央値をとって insert すれば平衡になる
            if seq:
                arranged = sorted(seq, key=itemgetter(depth % 2))
                mid = len(seq) // 2
                self.insert(seq[mid][0], seq[mid][1])
                self._balance_insert(arranged[:mid], depth+1)
                self._balance_insert(arranged[mid+1:], depth+1)


        def insert(self, x, y):
            """
            kD tree に値が (x, y) であるノードを O(depth) で挿入する
            (コンストラクタで生成した kD tree は平衡であることが保証されるが、insert により生成した部分の平衡性は保証されないことに注意)        
            """
            trailer = self.nil    # (x, y) を挿入するべき nil の一つ前のノードを保存するトレーラポインタ
            pos = self.root    # (x, y) を挿入するべき nil の場所を探す
            depth = 0
            while pos != self.nil:
                trailer = pos
                k, pos_k = (x, pos.x) if depth % 2 == 0 else (y, pos.y)
                if k < pos_k:
                    pos = pos.left
                elif pos_k < k:
                    pos = pos.right
                else:
                    pos.flag ^= pos.flag
                    pos = pos.left if pos.flag else pos.right
                depth += 1
            inserted_node = TwoDimNode(x, y, trailer, self.nil, self.nil)
            # trailer の depth
            depth -= 1
            k, trailer_k = (x, trailer.x) if depth % 2 == 0 else (y, trailer.y)
            # tree is empty
            if trailer == self.nil:
                self.root = inserted_node
            # どこかのノードの子供の位置に挿入する時
            elif k < trailer_k or (k == trailer_k and trailer.flag):
                trailer.left = inserted_node
            else:
                trailer.right = inserted_node
        
        def two_dim_search(self, sx, tx, sy, ty, node=None, depth=0):
            """
            kD tree に対し閉区間 D = {(x, y) | sx<=x<=tx, sy<=y<=ty} 内に存在する点を探してリストにまとめて返す (対応する点の個数 k として O(√n + k))
            下記のように検索必要性を判断し再帰的に左右の子に対し探索を行えば良い

            <-------- node.x -------->
            <----------->
            少しでも [sx,tx] が左側ゾーン ((-inf, node.x]) に被っていたら検索しておく必要がある
                        <----->
                        少しでも [sx, tx] が右側ゾーン ([node.x, inf)) に被っていたら検索しておく必要がある
            """        
            cnt = 0
            node = self.root if node is None else node
            # print(f"{node.x} {node.y}")
            if depth % 2 == 0:
                if node.left != self.nil and sx <= node.x:
                    cnt += self.two_dim_search(sx, tx, sy, ty, node.left, depth+1)
                if sx <= node.x <= tx and sy <= node.y <= ty:
                    cnt += 1
                if node.right != self.nil and tx >= node.x:
                    cnt += self.two_dim_search(sx, tx, sy, ty, node.right, depth+1)
            else:
                if node.left != self.nil and sy <= node.y:
                    cnt += self.two_dim_search(sx, tx, sy, ty, node.left, depth+1)
                if sx <= node.x <= tx and sy <= node.y <= ty:
                    cnt += 1
                if node.right != self.nil and ty >= node.y:
                    cnt += self.two_dim_search(sx, tx, sy, ty, node.right, depth+1)
            return cnt


    def unvisited_p(d, i, j):
        if i in d:
            if j in d[i]:
                return False
        return True

    def register(d, i, j):
        if i not in d:
            d[i] = set()
            d[i].add(j)
        else:
            d[i].add(j)

    
    h, w, n = mi()
    points = [lmi() for _ in range(n)]
    shuffle(points)

    num_of_grids_contains_black = [0] * 10

    # kD tree 処理
    kd_tree = TwoDimTree()
    for x, y in points:
        kd_tree.insert(x, y)

    d = dict()
    for x, y in points:
        # print(f"{x} {y} {kd_tree.two_dim_search(x-1, x+1, y-1, y+1)}")
        for i in range(x-1, x+2):
            for j in range(y-1, y+2):
                if 2 <= i <= h-1 and 2 <= j <= w-1 and unvisited_p(d, i, j):    # 探索する 3*3 grid のセンター
                    num_of_grids_contains_black[kd_tree.two_dim_search(i-1, i+1, j-1, j+1)] += 1
                    register(d, i, j)


    num_of_grids_contains_black[0] = (h - 2) * (w - 2) - sum(num_of_grids_contains_black[1:])
    print(*num_of_grids_contains_black, sep='\n')



if __name__ == "__main__":
    main()

Buggy submission (verdict: Runtime Error):
#!/usr/bin/env python3

import sys
# import math
# from string import ascii_lowercase, ascii_uppercase, ascii_letters, digits, hexdigits
# import re                                    # re.compile(pattern) => ptn obj; p.search(s), p.match(s), p.finditer(s) => match obj; p.sub(after, s)
# from operator import itemgetter              # itemgetter(1), itemgetter('key')
# from collections import deque                # deque class. deque(L): dq.append(x), dq.appendleft(x), dq.pop(), dq.popleft(), dq.rotate()
# from collections import defaultdict          # subclass of dict. defaultdict(facroty)
# from collections import Counter              # subclass of dict. Counter(iter): c.elements(), c.most_common(n), c.subtract(iter)
# from heapq import heapify, heappush, heappop # built-in list. heapify(L) changes list in-place to min-heap in O(n), heappush(heapL, x) and heappop(heapL) in O(lgn).
# from heapq import nlargest, nsmallest        # nlargest(n, iter[, key]) returns k-largest-list in O(n+klgn).
# from itertools import count, cycle, repeat   # count(start[,step]), cycle(iter), repeat(elm[,n])
# from itertools import groupby                # [(k, list(g)) for k, g in groupby('000112')] returns [('0',['0','0','0']), ('1',['1','1']), ('2',['2'])]
# from itertools import starmap                # starmap(pow, [[2,5], [3,2]]) returns [32, 9]
# from itertools import product, permutations  # product(iter, repeat=n), permutations(iter[,r])
# from itertools import combinations, combinations_with_replacement
# from itertools import accumulate             # accumulate(iter[, f])
# from functools import reduce                 # reduce(f, iter[, init])
# from functools import lru_cache              # @lrucache ...arguments of functions should be able to be keys of dict (e.g. list is not allowed)
# from bisect import bisect_left, bisect_right # bisect_left(a, x, lo=0, hi=len(a)) returns i such that all(val<x for val in a[lo:i]) and all(val>-=x for val in a[i:hi]).
# from copy import deepcopy                    # to copy multi-dimentional matrix without reference
# from fractions import gcd                    # for Python 3.4 (previous contest @AtCoder)
from random import shuffle

def main():
    mod = 1000000007                # 10^9+7
    inf = float('inf')              # sys.float_info.max = 1.79...e+308
    # inf = 2 ** 64 - 1               # (for fast JIT compile in PyPy) 1.84...e+19
    sys.setrecursionlimit(10**6)    # 1000 -> 1000000
    def input(): return sys.stdin.readline().rstrip()
    def ii():    return int(input())
    def mi():    return map(int, input().split())
    def mi_0():  return map(lambda x: int(x)-1, input().split())
    def lmi():   return list(map(int, input().split()))
    def lmi_0(): return list(map(lambda x: int(x)-1, input().split()))
    def li():    return list(input())
    

    class TwoDimNode:
        def __init__(self, x=None, y=None, parent=None, left=None, right=None):
            self.x = x
            self.y = y
            self.parent = parent
            self.left = left
            self.right = right
            self.flag = True

    class TwoDimTree:
        def __init__(self):
            self.nil = TwoDimNode()
            self.nil.parent = self.nil
            self.nil.left = self.nil
            self.nil.right = self.nil
            self.root = self.nil
        
        def preorder_traverse(self, node=None):
            if node is None:
                node = self.root
            if node != self.nil:
                print(f"({node.x},{node.y})", end=' ')
                self.preorder_traverse(node=node.left)
                self.preorder_traverse(node=node.right)

        def post_order_traverse(self, node=None):
            if node is None:
                node = self.root
            if node != self.nil:
                self.post_order_traverse(node=node.left)
                self.post_order_traverse(node=node.right)
                print(f"({node.x},{node.y})", end=' ')
                
        def insert(self, x, y):
            trailer = self.nil
            pos = self.root
            depth = 0
            while pos != self.nil:
                trailer = pos
                if depth % 2 == 0:
                    k, pos_k = x, pos.x
                else:
                    k, pos_k = y, pos.y
                if k < pos_k:
                    pos = pos.left
                elif pos_k < k:
                    pos = pos.right
                else:
                    pos.flag ^= pos.flag
                    pos = pos.left if pos.flag else pos.right
                depth += 1
            inserted_node = TwoDimNode(x, y, trailer, self.nil, self.nil)
            # trailer の depth
            depth -= 1
            if depth % 2 == 0:
                k, trailer_k = x, trailer.x
            else:
                k, trailer_k = y, trailer.y
            # tree is empty
            if trailer == self.nil:
                self.root = inserted_node
            elif k < trailer_k or (k == trailer_k and trailer.flag):
                trailer.left = inserted_node
            else:
                trailer.right = inserted_node
        
        def two_dim_search(self, sx, tx, sy, ty, node=None, depth=0):
            buf = []
            if node is None:
                node = self.root
            # print(f"{node.x} {node.y}")
            if depth % 2 == 0:
                if node.left != self.nil and sx <= node.x:
                    buf += self.two_dim_search(sx, tx, sy, ty, node.left, depth+1)
                if sx <= node.x <= tx and sy <= node.y <= ty:
                    buf.append((node.x, node.y))
                if node.right != self.nil and tx >= node.x:
                    buf += self.two_dim_search(sx, tx, sy, ty, node.right, depth+1)
            else:
                if node.left != self.nil and sy <= node.y:
                    buf += self.two_dim_search(sx, tx, sy, ty, node.left, depth+1)
                if sx <= node.x <= tx and sy <= node.y <= ty:
                    buf.append((node.x, node.y))
                if node.right != self.nil and ty >= node.y:
                    buf += self.two_dim_search(sx, tx, sy, ty, node.right, depth+1)
            return buf

    def unvisited_p(d, i, j):
        if i in d:
            if j in d[i]:
                return False
        return True

    def register(d, i, j):
        if i not in d:
            d[i] = set()
            d[i].add(j)
        else:
            d[i].add(j)

    
    h, w, n = mi()
    points = [lmi() for _ in range(n)]
    shuffle(points)

    num_of_grids_contains_black = [0] * 10

    # kD tree 処理
    kd_tree = TwoDimTree()
    for x, y in points:
        kd_tree.insert(x, y)
    
    # kd_tree.preorder_traverse()
    # print('')
    # kd_tree.post_order_traverse()
    # print('')



    d = dict()
    for x, y in points:
        # print(f"{x} {y} {kd_tree.two_dim_search(x-1, x+1, y-1, y+1)}")
        for i in range(x-1, x+2):
            for j in range(y-1, y+2):
                if 2 <= i <= h-1 and 2 <= j <= w-1 and unvisited_p(d, i, j):    # 探索する 3*3 grid のセンター
                    # print(f"{i} {j}")
                    # print(kd_tree.two_dim_search(i-1, i+1, j-1, j+1))
                    num_of_grids_contains_black[len(kd_tree.two_dim_search(i-1, i+1, j-1, j+1))] += 1
                    register(d, i, j)


    num_of_grids_contains_black[0] = (h - 2) * (w - 2) - sum(num_of_grids_contains_black[1:])
    print(*num_of_grids_contains_black, sep='\n')



if __name__ == "__main__":
    main()

Buggy submission (verdict: Runtime Error):
#!/usr/bin/env python3

import sys
# import math
# from string import ascii_lowercase, ascii_uppercase, ascii_letters, digits, hexdigits
# import re                                    # re.compile(pattern) => ptn obj; p.search(s), p.match(s), p.finditer(s) => match obj; p.sub(after, s)
# from operator import itemgetter              # itemgetter(1), itemgetter('key')
# from collections import deque                # deque class. deque(L): dq.append(x), dq.appendleft(x), dq.pop(), dq.popleft(), dq.rotate()
# from collections import defaultdict          # subclass of dict. defaultdict(facroty)
# from collections import Counter              # subclass of dict. Counter(iter): c.elements(), c.most_common(n), c.subtract(iter)
# from heapq import heapify, heappush, heappop # built-in list. heapify(L) changes list in-place to min-heap in O(n), heappush(heapL, x) and heappop(heapL) in O(lgn).
# from heapq import nlargest, nsmallest        # nlargest(n, iter[, key]) returns k-largest-list in O(n+klgn).
# from itertools import count, cycle, repeat   # count(start[,step]), cycle(iter), repeat(elm[,n])
# from itertools import groupby                # [(k, list(g)) for k, g in groupby('000112')] returns [('0',['0','0','0']), ('1',['1','1']), ('2',['2'])]
# from itertools import starmap                # starmap(pow, [[2,5], [3,2]]) returns [32, 9]
# from itertools import product, permutations  # product(iter, repeat=n), permutations(iter[,r])
# from itertools import combinations, combinations_with_replacement
# from itertools import accumulate             # accumulate(iter[, f])
# from functools import reduce                 # reduce(f, iter[, init])
# from functools import lru_cache              # @lrucache ...arguments of functions should be able to be keys of dict (e.g. list is not allowed)
# from bisect import bisect_left, bisect_right # bisect_left(a, x, lo=0, hi=len(a)) returns i such that all(val<x for val in a[lo:i]) and all(val>-=x for val in a[i:hi]).
# from copy import deepcopy                    # to copy multi-dimentional matrix without reference
# from fractions import gcd                    # for Python 3.4 (previous contest @AtCoder)
from random import shuffle

def main():
    mod = 1000000007                # 10^9+7
    inf = float('inf')              # sys.float_info.max = 1.79...e+308
    # inf = 2 ** 64 - 1               # (for fast JIT compile in PyPy) 1.84...e+19
    sys.setrecursionlimit(10**6)    # 1000 -> 1000000
    def input(): return sys.stdin.readline().rstrip()
    def ii():    return int(input())
    def mi():    return map(int, input().split())
    def mi_0():  return map(lambda x: int(x)-1, input().split())
    def lmi():   return list(map(int, input().split()))
    def lmi_0(): return list(map(lambda x: int(x)-1, input().split()))
    def li():    return list(input())
    

    class TwoDimNode:
        def __init__(self, x=None, y=None, parent=None, left=None, right=None):
            self.x = x
            self.y = y
            self.parent = parent
            self.left = left
            self.right = right
            self.flag = True

    class TwoDimTree:
        def __init__(self):
            self.nil = TwoDimNode()
            self.nil.parent = self.nil
            self.nil.left = self.nil
            self.nil.right = self.nil
            self.root = self.nil
        
        def preorder_traverse(self, node=None):
            if node is None:
                node = self.root
            if node != self.nil:
                print(f"({node.x},{node.y})", end=' ')
                self.preorder_traverse(node=node.left)
                self.preorder_traverse(node=node.right)

        def post_order_traverse(self, node=None):
            if node is None:
                node = self.root
            if node != self.nil:
                self.post_order_traverse(node=node.left)
                self.post_order_traverse(node=node.right)
                print(f"({node.x},{node.y})", end=' ')
                
        def insert(self, x, y):
            trailer = self.nil
            pos = self.root
            depth = 0
            while pos != self.nil:
                trailer = pos
                if depth % 2 == 0:
                    k, pos_k = x, pos.x
                else:
                    k, pos_k = y, pos.y
                if k < pos_k:
                    pos = pos.left
                elif pos_k < k:
                    pos = pos.right
                else:
                    pos.flag ^= pos.flag
                    pos = pos.left if pos.flag else pos.right
                depth += 1
            inserted_node = TwoDimNode(x, y, trailer, self.nil, self.nil)
            # trailer の depth
            depth -= 1
            if depth % 2 == 0:
                k, trailer_k = x, trailer.x
            else:
                k, trailer_k = y, trailer.y
            # tree is empty
            if trailer == self.nil:
                self.root = inserted_node
            elif k < trailer_k or (k == trailer_k and trailer.flag):
                trailer.left = inserted_node
            else:
                trailer.right = inserted_node
        
        def two_dim_search(self, sx, tx, sy, ty, node=None, depth=0):
            buf = []
            if node is None:
                node = self.root
            # print(f"{node.x} {node.y}")
            if depth % 2 == 0:
                if node.left != self.nil and sx <= node.x:
                    buf += self.two_dim_search(sx, tx, sy, ty, node.left, depth+1)
                if sx <= node.x <= tx and sy <= node.y <= ty:
                    buf.append((node.x, node.y))
                if node.right != self.nil and tx >= node.x:
                    buf += self.two_dim_search(sx, tx, sy, ty, node.right, depth+1)
            else:
                if node.left != self.nil and sy <= node.y:
                    buf += self.two_dim_search(sx, tx, sy, ty, node.left, depth+1)
                if sx <= node.x <= tx and sy <= node.y <= ty:
                    buf.append((node.x, node.y))
                if node.right != self.nil and ty >= node.y:
                    buf += self.two_dim_search(sx, tx, sy, ty, node.right, depth+1)
            return buf

    def unvisited_p(d, i, j):
        if i in d:
            if j in d[i]:
                return False
        return True

    def register(d, i, j):
        if i not in d:
            d[i] = set()
            d[i].add(j)
        else:
            d[i].add(j)

    
    h, w, n = mi()
    points = [lmi() for _ in range(n)]
    shuffle(points)

    num_of_grids_contains_black = [0] * 10

    # kD tree 処理
    kd_tree = TwoDimTree()
    for x, y in points:
        kd_tree.insert(x, y)
    
    # kd_tree.preorder_traverse()
    # print('')
    # kd_tree.post_order_traverse()
    # print('')



    d = dict()
    for x, y in points:
        # print(f"{x} {y} {kd_tree.two_dim_search(x-1, x+1, y-1, y+1)}")
        for i in range(x-1, x+2):
            for j in range(y-1, y+2):
                if 2 <= i <= h-1 and 2 <= j <= w-1 and unvisited_p(d, i, j):    # 探索する 3*3 grid のセンター
                    # print(f"{i} {j}")
                    # print(kd_tree.two_dim_search(i-1, i+1, j-1, j+1))
                    num_of_grids_contains_black[len(kd_tree.two_dim_search(i-1, i+1, j-1, j+1))] += 1
                    register(d, i, j)


    num_of_grids_contains_black[0] = (h - 2) * (w - 2) - sum(num_of_grids_contains_black[1:])
    print(*num_of_grids_contains_black, sep='\n')



if __name__ == "__main__":
    main()