Problem:


Score : 400 points

Problem Statement

Given is a number sequence A of length N.

Find the number of integers i \left(1 \leq i \leq N\right) with the following property:

For every integer j \left(1 \leq j \leq N\right) such that i \neq j , A_j does not divide A_i.

Constraints

All values in input are integers.

1 \leq N \leq 2 \times 10^5

1 \leq A_i \leq 10^6

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \cdots A_N

Output

Print the answer.

Sample Input 1

5
24 11 8 3 16

Sample Output 1

3

The integers with the property are 2, 3, and 4.

Sample Input 2

4
5 5 5 5

Sample Output 2

0

Note that there can be multiple equal numbers.

Sample Input 3

10
33 18 45 28 8 19 89 86 2 4

Sample Output 3

5



Sample input:
5
24 11 8 3 16


Sample output:
3

Submission status: Wrong Answer

Solution code:
def main(sample_file = ''):

    """ convenient functions
    # for i, a in enumerate(iterable)
    # q, mod = divmod(a, b)
    # divmod(x, y) returns the tuple (x//y, x%y)
    # Higher-order function: reduce(operator.mul, xyz_count, 1)
    # manage median(s) using two heapq https://atcoder.jp/contests/abc127/tasks/abc127_f
    """

    """convenient decorator
    # @functools.lru_cache():
    # to facilitate use of recursive function
        # ex:
        # from functools import lru_cache
        # import sys
        # sys.setrecursionlimit(10**9)
        # @lru_cache(maxsize=None)
        # def fib(n):
        #     if n < 2:
        #         return n
        #     return fib(n-1) + fib(n-2)
        # print(fib(1000))
    """
    
    # import numpy as np
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product # https://docs.python.org/ja/3/library/itertools.html
    # accumulate() returns iterator! to get list: list(accumulate())
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  # prime factor
        b, e = 2, 0  # base, exponent
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):   
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        # TODO: How should I do when n - r is negative?
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict # https://docs.python.org/ja/3/library/collections.html#collections.deque
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest # https://docs.python.org/ja/3/library/heapq.html
    from copy import deepcopy, copy # https://docs.python.org/ja/3/library/copy.html
    import operator
    from operator import itemgetter #sort 
    # ex1: List.sort(key=itemgetter(1))
    # ex2: sorted(tuples, key=itemgetter(1,2))
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd # Deprecated since version 3.5: Use math.gcd() instead.
    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)
    def make_divisors(n, reversed=False):
        """create list of divisors
        
        Args:
            number (int): number from which list of divisors is created
            reversed (bool, optional): ascending order if False. Defaults to False.
        
        Returns:
            list: list of divisors
        """
        divisors = set()
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.add(i)
                divisors.add(n//i)
        return sorted(list(divisors),reverse=reversed)
    
    # first create factorial_list
    # fac_list = modfactorial_list(n)
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    AtoZ = list('abcdefghijklmnopqrsruvwxyz') # 26
    modpow = lambda a, n, p = MOD: pow(a, n, p) # Recursive function in python is slow!
    def modinv(a, p = MOD):
        # evaluate reciprocal using Fermat's little theorem:
        # a**(p-1) is identical to 1 (mod p) when a and p is coprime
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        # fac_list = modfactorial_list(100)
        # print(modcomb(100, 5, modfactorial_list(100)))
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    class UnionFindTree:
        """union find tree class
        TODO: fix this description...
        how to use (example):
        >>  uf = UnionFindTree(N) 
        >>  if uf.find_root(a) == uf.find_root(b):
        >>      do something
        >>  else:
        >>      do something
        >>      uf.unite(a, b)
        """
        def __init__(self, N):
            self.root = [-1] * (N+1)
            self.rank   = [0]  * (N+1)
            self.connected_num = [1] * (N+1)
    
        def find_root(self,x):
            root = self.root
            while root[x] != -1:
                x = root[x]
            return x
    
        def unite(self,x,y):
            root = self.root
            rank = self.rank
            connected_num = self.connected_num
            find_root = self.find_root
    
            rx = find_root(x)
            ry = find_root(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    root[rx] = ry
                    rx,ry = ry,rx
                else:
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                    root[ry] = rx       
                connected_num[rx] += connected_num[ry]

    class SegTree:
        """
        ref: https://qiita.com/takayg1/items/c811bd07c21923d7ec69
        init(init_val, ide_ele): 配列init_valで初期化 O(N)
        update(k, x): k番目の値をxに更新 O(logN)
        query(l, r): 区間[l, r)をsegfuncしたものを返す O(logN)
        """
        def __init__(self, init_val, segfunc, ide_ele):
            """
            init_val: 配列の初期値
            segfunc: 区間にしたい操作
            ide_ele: 単位元
            n: 要素数
            num: n以上の最小の2のべき乗
            tree: セグメント木(1-index)
            """
            n = len(init_val)
            self.segfunc = segfunc
            self.ide_ele = ide_ele
            self.num = 1 << (n - 1).bit_length()
            self.tree = [ide_ele] * 2 * self.num
            # 配列の値を葉にセット
            for i in range(n):
                self.tree[self.num + i] = init_val[i]
            # 構築していく
            for i in range(self.num - 1, 0, -1):
                self.tree[i] = self.segfunc(self.tree[2 * i], self.tree[2 * i + 1])

        def update(self, k, x):
            """
            k番目の値をxに更新
            k: index(0-index)
            x: update value
            """
            k += self.num
            self.tree[k] = x
            while k > 1:
                self.tree[k >> 1] = self.segfunc(self.tree[k], self.tree[k ^ 1])
                k >>= 1

        def query(self, l, r):
            """
            [l, r)のsegfuncしたものを得る
            l: index(0-index)
            r: index(0-index)
            """
            res = self.ide_ele
            l += self.num
            r += self.num
            while l < r:
                if l & 1:
                    res = self.segfunc(res, self.tree[l])
                    l += 1
                if r & 1:
                    res = self.segfunc(res, self.tree[r - 1])
                l >>= 1
                r >>= 1
            return res

    # ************ Graph ************
    # Graph: https://en.wikipedia.org/wiki/Directed_graph
    # 最短経路問題: https://ja.wikipedia.org/wiki/%E6%9C%80%E7%9F%AD%E7%B5%8C%E8%B7%AF%E5%95%8F%E9%A1%8C
    
    # Bellman-Ford: O(|V||E|). Use this if there exists an edge with negative length in the graph
    # After N steps, the shortest path has converded if there doesn't exist an cycle of edges with negative
    # Watch out: d[N] == d[2*N] doesn't necessarily mean the graph doesn't have negative cycle
    # ref: https://www.youtube.com/watch?v=1Z6ofKN03_Y

    def BellmanFord(N, M, ABC, vertex_start, vertex_end, value_if_inf = -1, find_shortest = False):
        """to calculate furthest or shortest length between vertex_start and vertex_end using BellmanFord algorithm
        
        Args:
            N (int): number of vertices
            M (int): number of edges
            ABC (list): [(ai, bi, ci) for _ in range(N)] where i-th edge is directed from vertex ai to vertex bi and the length is ci 
            vertex_start (int): start vertex. usually use 0.
            vertex_end (int): end vertex. usually use N-1.
            value_if_inf (int or string as you like, optional): value you want when the furthest (or shortest) distance is infinite (or -infinite). Defaults to -1.
            find_shortest (bool, optional): choose False to find furthest path. Defaults to False.
        
        Returns:
            int or string: normally int (but can be str if you set value_if_inf to str)
            
        Example:
                N, M, P = R()
                ABC = [R() for _ in range(M)]
                ABC = [(a-1, b-1, c-P) for a, b, c in ABC]
                print(BellmanFord(N, M, ABC, 0, N-1, value_if_inf = 'inf'))

        """

        def make_reachable_list(N, M, ABC, vertex_start, vertex_end):
            reachable_to_direct = defaultdict(list)
            reachable_from_direct = defaultdict(list)
            reachable_from_start = [False] * N
            reachable_to_end = [False] * N
            reachable_from_start[vertex_start] = True
            reachable_to_end[vertex_end] = True
            reachable_from_both_sides = [False] * N
            dfs_from_start = []
            dfs_to_end = []
            for a, b, c in ABC:
                reachable_to_direct[a].append(b)
                reachable_from_direct[b].append(a)
                if a == vertex_start:
                    dfs_from_start.append(b)
                    reachable_from_start[b] = True
                if b == vertex_end:
                    dfs_to_end.append(a)
                    reachable_to_end[a] = True
            while dfs_from_start:
                v = dfs_from_start.pop()
                for i in reachable_to_direct[v]:
                    if not reachable_from_start[i]:
                        reachable_from_start[i] = True
                        dfs_from_start.append(i)
            while dfs_to_end:
                v = dfs_to_end.pop()
                for i in reachable_from_direct[v]:
                    if not reachable_to_end[i]:
                        reachable_to_end[i] = True
                        dfs_to_end.append(i)
            for i in range(N):
                reachable_from_both_sides[i] = reachable_from_start[i] and reachable_to_end[i]
            return reachable_from_both_sides
        
        reachable_from_both_sides = make_reachable_list(N, M, ABC, vertex_start, vertex_end)
        
        if find_shortest:
            dist = [INF for i in range(N)]
        else:
            dist = [-INF for i in range(N)]
        
        dist[vertex_start] = 0
        for i in range(N):
            updated = False
            for a, b, c in ABC:
                if not reachable_from_both_sides[a]:
                    continue
                elif find_shortest:
                    update_condition = dist[a] + c < dist[b]
                else:
                    update_condition = dist[a] + c > dist[b]
                if dist[a] != INF and update_condition:
                    dist[b] = dist[a] + c
                    updated = True
                    if i == N-1:
                        return value_if_inf
            if not updated:
                break
        return dist[vertex_end]

    # Warshall Floyd O(V**3)
    def warshall_floyd(number_vertex, XYD, shift_one_for_vertex=False):
        # ref: https://juppy.hatenablog.com/entry/2018/11/01/%E8%9F%BB%E6%9C%AC_python_%E5%85%A8%E7%82%B9%E5%AF%BE%E6%9C%80%E7%9F%AD%E7%B5%8C%E8%B7%AF%E6%B3%95%EF%BC%88%E3%83%AF%E3%83%BC%E3%82%B7%E3%83%A3%E3%83%AB%E3%83%95%E3%83%AD%E3%82%A4%E3%83%89%E6%B3%95
        # number_vertex: len(vertex)
        # XYD: list of distance from x to y
        # shift_one_for_vertex: XYDの値が1~Nの時(0~N-1でない時)に調整するフラグ。
        # d[i][j]: iからjへの最短距離
        d = [[float("inf")]*number_vertex for i in range(number_vertex)]
        for x, y, dist in XYD:
            if shift_one_for_vertex:
                x = x - 1
                y = y - 1
            d[x][y] = dist
            d[y][x] = dist
        for i in range(number_vertex):
            d[i][i] = 0 # distance of same vertex is 0
        for k in range(number_vertex):
            for i in range(number_vertex):
                for j in range(number_vertex):
                    d[i][j] = min(d[i][j],d[i][k] + d[k][j])
        return d


    """ initialize variables and set inputs
    # initialize variables
        # to initialize list, use [0] * n
        # to initialize two dimentional array:
            # ex) [[0] * N for _ in range(N)]
            # ex2) dp = [[0] * (N+1) for _ in range(W*2)]
    # set inputs
        # put inputs between specific values (almost as quickly)
        # ex) S = [-INF] + [int(r()) for _ in range(A)] + [INF]
        # open(0).read() is sometimes useful:
        # ex) n, m, *x = map(int, open(0).read().split())
        #     min(x[::2]) - max(x[1::2])
        # ex2) *x, = map(int, open(0).read().split())
        #     don't forget to add comma after *x if only one variable is used
    # preprocessing
        # transpose = [x for x in zip(*data)]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [(1, 4, 7), (2, 5, 8), (3, 6, 9)]
        # flat = [flatten for inner in data for flatten in inner]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [1, 2, 3, 4, 5, 6, 7, 8, 9]
    # calculate and output
        # output pattern
        # ex1) print(*l) => when l = [2, 5, 6], printed 2 5 6
    """

    # functions to read input
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    r_float = lambda: float(r())
    R = lambda: list(map(int, r().split()))
    R_str = lambda: r().split()
    R_map = lambda: map(int, r().split())
    R_float = lambda: list(map(float, r().split()))
    R_tuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    # single int: int(r())
    # single string: r()
    # single float: float(r())
    # line int: R()
    # line string: r().split()
    # line (str, int, int): [j if i == 0 else int(j) for i, j in enumerate(r().split())]
    # lines int: [R() for _ in range(n)]
    """

    # for test
    if sample_file:
        sys.stdin = open(sample_file)
        
    # ----------------------------------
    # main
    #%%
    N = r_int()
    A = R()
    A.sort()
    s = []
    ans = 0

    for i, a in enumerate(A):
        if i == N-1 or (i != N-1 and A[i] != A[i+1]):
            fac_list = make_divisors(a)
            flag = 0
            for ss in s:
                if a%ss == 0:
                    flag = 1
                    break
                elif ss ** 2 > a:
                    break
            if flag == 0:
                ans += 1
        s.append(a)

    print(ans)

    #%%
    # end of main
    # ----------------------------------

    """memo: how to use defaultdict of list
    # initialize
    Dic = defaultdict(list)
    # append / extend
    Dic[x].append(y)
    # three methods for loop: keys(), values(), items()
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    # to make binary digits text
    >>> a = 5
    >>> bin_str_a = format(a, '#06b')
    >>> print(bin_str_a)
    0b0101 # first 2 strings (='0b') indicates it is binary
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()

Submission status: Wrong Answer

Solution code:
import numpy as np
N = int(input())
A = list(map(float, input().split()))
B = np.zeros(100)
D= np.ones(N)
f= 0
for i in range(2, 101):
    j=0
    c = 1
    while j<len(A):
        if A[j] % i == 0:
            A.pop(j)
            j -=1
            if c == 1:
                f += 1
                c = 0
        j += 1
q = f+len(A)
if q < 2:
    print(0)
else:
    print(q)

Submission status: Wrong Answer

Solution code:
import sys
sys.setrecursionlimit(10 ** 7)
input = sys.stdin.readline
INF = float('inf')
from collections import defaultdict
dic = defaultdict(lambda:INF)

used = defaultdict(lambda:0)
remove = defaultdict(lambda:0)

n = int(input())
a = list(map(int, input().split()))
a.sort()

cnt1 = a.count(1)
if cnt1 == 1:
    print(1)
    exit()
elif cnt1 >1:
    print(0)
    exit()

from collections import Counter
def prime_factorize(n):
    d = Counter()
    m = 2
    while m*m <= n:
        while n%m == 0:
            n //= m
            d[m] += 1
        m += 1
    if n > 1:
        d[n] += 1
    return d

for aa in a:
    if used[aa]==1:
        remove[aa]=1
        continue
    c = prime_factorize(aa)
    flg = True
    for k in c.keys():
        if dic[k] == INF:
            dic[k] = aa//k
        elif (aa//k)%dic[k]==0:
            flg = False

    if flg:
        used[aa]=1

ans = sum(list(used.values()))-sum(list((remove.values())))
print(ans)

Submission status: Wrong Answer

Solution code:
import heapq

n = int(input())
a = [int(i) for i in input().split()]
sa = list(set(a))
heapq.heapify(sa)
div = []
ans = 0
while sa:
    i = heapq.heappop(sa)
    if a.count(i) > 1:
        continue
    div.append(i)
    for d in div:
        if d == i:
            ans += 1
            break
        elif i % d == 0:
            break
print(ans)

Submission status: Wrong Answer

Solution code:
import copy
N = int(input())
A = sorted([ int(i) for i in input().strip().split(' ')])
n = [ i for i in range(N) ]
B = [0] * N

for i in n:
#    if B[i] != 0:
#        continue
    n.remove(i)
    for j in copy.copy(n):
        if A[i] == A[j]:
            B[i] = 1
            B[j] = 1
            n.remove(j)
        elif A[j] % A[i] == 0:
            B[j] = 1
            n.remove(j)

print(N - sum(B))

Submission status: Wrong Answer

Solution code:
import math
N=int(input())
sum=0
array= input().split(" ")
for i in range(N):
  num=int(array[i])
  yakusuu_array = []



  for j in range(1,num):

      if num % j == 0:

          yakusuu_array.append(str(j))
  yakusuu_array.append(str(num))

  if len(list(set(array) & set(yakusuu_array)))!=1:
      sum=sum+1
print(sum)

Submission status: Wrong Answer

Solution code:
n = int(input())
a = list(map(int, input().strip().split()))
a.sort()
MAX = max(a)
f = [0] * (MAX + 2)
g = [0] * (MAX + 2)

ans = [0] * (MAX + 2)
for i in range(n):
    g[a[i]] += 1
    x = a[i]
    inc = a[i]
    if f[x] == 0:
        ans[a[i]] += 1
        
    while x <= MAX:            
        if f[x] >= 1:
            break
        else:
            f[x] += 1
            x += inc

ans_count = 0
for i in range(n):
    if g[a[i]] == 1 and ans[a[i]] == 1:
        ans_count += 1
        #print(a[i])
print(ans_count)

Submission status: Wrong Answer

Solution code:
#import sympy
#sympy.divisors(10**9)
n = int(input())

a = list(map(int, input().split()))

a.sort(reverse = True)

def make_divisors(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)

    divisors.sort()
    return divisors

if len(set(a)) == 1:
    print(0)
else:
    
    
    ans = 0

    for i in range(n):
        target = make_divisors(a[i])
        if len(set(target) & set(a)) == 1:
            ans += 1

    print(ans)

Submission status: Wrong Answer

Solution code:
import math

def make_prime_list_2(num):
    if num < 2:
        return []

    # 0のものは素数じゃないとする
    prime_list = [i for i in range(num + 1)]
    prime_list[1] = 0 # 1は素数ではない
    num_sqrt = math.sqrt(num)

    for prime in prime_list:
        if prime == 0:
            continue
        if prime > num_sqrt:
            break

        for non_prime in range(2 * prime, num, prime):
            prime_list[non_prime] = 0

    return [prime for prime in prime_list if prime != 0]

prime = make_prime_list_2(10**6) + [1]

n = int(input())
l = list(map(int,input().split()))
#print(n)
#print(l)

if len(set(l)) == 1:
    print(0)
    exit()


l_2 = []
ans = 0
for _ in l:
    if _ in prime:
        ans += 1
    else:
        l_2.append(_)
tmp = len(l_2)
#print(l_2, ans, tmp)

for i in range(tmp):
    for j in range(n):
        if i != j:
            if l_2[i] % l[j] == 0:
                break
    else:
        ans += 1

print(ans)

Submission status: Wrong Answer

Solution code:
import copy

n = int(input())
a = list(map(int, input().split( )))

count = 0

for i in range(n-1):
    c_ = 0
    a_ = copy.copy(a)
    del a_[i]
    for j in a_:
        if  (a[i] % j) == 0:
            break
        else:
            c_ += 1
        if c_ == (n - 1):
            count += 1

print(count)

Submission status: Wrong Answer

Solution code:
from collections import defaultdict
n = int(input())
a = sorted(list({int(i) for i in input().split()}))
dic = defaultdict(lambda : 0)
nums = defaultdict(lambda : 0)
def decomp(i):
    d = defaultdict(lambda : 0)
    sqrt = round(i ** 0.5 + 0.5)
    for j in range(2, sqrt + 1):
        count = 0
        n = i
        if not i % j:
            while i % j == 0:
                count += 1
                i //= j
                d[j] = count
                if not dic[j]:
                    dic[j] = count
                    nums[j] = n
                else:
                    if count < dic[j]:
                        dic[j] = count
                        nums[j] = n
    if i != 1:
        d[i] = 1
        if not dic[i]:
            dic[i] = 1
            nums[i] = n
    return d
p = [decomp(i) for i in a]
count = 0
for i, j in enumerate(p):
    for k, l in j.items():
        if nums[k] == a[i]:
            count += 1
        else:
            if l >= dic[k]:
                pass
            else:
                count += 1
print(count)

Submission status: Wrong Answer

Solution code:
n = int(input())
a = list(map(int, input().split()))
counter = 0
sn_list = sorted(a)
#print(sn_list)
for i in range(n):
  flag = True
  for j in range(n - i):
    if sn_list[j] % sn_list[i] == 0:
      #print(i, j, sn_list[i], sn_list[j])
      flag = False
      break
  if flag:
    #print('*', i, sn_list[i])
    counter += 1
print(counter)

Submission status: Wrong Answer

Solution code:
def make_divisors(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)
    return sorted(divisors, reverse=True)


N = int(input())
A = list(map(int, input().split()))

if N == 1:
    print(1)
    exit()
    
A = sorted(A)
check_list = [0] * (10**6 + 1)

for a in A:
    check_list[a] = 1

cnt = 0
prev_val = -1
next_val = A[1]
for i in range(len(A)):
    if len(A) - 1 == i:
        if prev_val == A[i]:
            continue        
        prev_val = A[i]
    else:
        if next_val == A[i]:
            continue
        next_val = A[i + 1]
    divisors = make_divisors(A[i])[1:-1]
    check_ok = True
    for d in divisors:
       if check_list[d] == 1:
           check_ok = False
    if check_ok == True:
        cnt += 1
print(cnt)

Submission status: Wrong Answer

Solution code:
import math

def isPrime(n):
  if n == 1:
    return False
  for k in range(2, int(math.sqrt(n)) + 1):
    if n % k == 0:
      return False
  return True

def isDiv(x, y):
  if x % y == 0:
    return True
  else:
    return False

N = int(input())
A = sorted(list(map(int, input().split())))
cnt = N

if len(A) == 1:
  print(N)
  exit()

if A[0] == 1 and A[1] == 1:
  print(N)
  exit()
if A[0] == 1 and A[1] != 1:
  print(N - 1)
  exit()

for i in range(N):
  x = A[i]
  if isPrime(x):
    if i - 1 >= 0:
      y = A[i - 1]
      if isDiv(x, y):
        cnt -= 1
        continue
    if i + 1 < N:
      y = A[i + 1]
      if isDiv(x, y):
        cnt -= 1
        continue
    continue
    
  for j in range(i):
    y = A[j]
    if isDiv(x, y):
      cnt -= 1
      break
print(cnt)

Submission status: Wrong Answer

Solution code:
from collections import Counter
N=int(input())
list = list(map(int, input().split()))
list.sort()
ans=0
counter = Counter(list)
rlist=counter.most_common()
a=rlist[0][1]
ans+=a
while rlist[0][0] in list:
  list.remove(rlist[0][0])
for i in range (0,N-a):
  res=0
  for j in range(0,N-a):
    if(i!=j):
      if(list[i] % list[j]==0):
        res+=1
        break
  if(0<res):
    ans+=1
print(N-ans)

Submission status: Wrong Answer

Solution code:
N = int(input())
P = sorted(map(int,input().split()))
R = [0]*N
Q = sorted(list(set(P)))
if Q.count(1) == 1:
    print(1)
elif Q.count(1) > 1:
    print(0)
elif len(Q) == 1:
    print(0)
else:
    for i in range (N):
        for j in range (N-i+1):
            if (j + i -1) != i:
                if R[j + i -1] == 0:
                    if (P[j+i-1] % P[i]) == 0:
                        R[j+i-1] = 1
    print(R.count(0))

Submission status: Wrong Answer

Solution code:
# 2020/06/14
# AtCoder Beginner Contest 170 - D

# Input
n = int(input())
a = list(map(int,input().split()))
a.sort()
a.append(10**7)
sosulist = list()
sosulist.append(0)

# Calc
ans = n

if a[0] == a[1]:
    ans = ans - 1

for i in range(1, n):
    if a[i] == a[i+1]:
        ans = ans - 1
        sosulist.append(i)

    else:
        wkval = 1
        slen = len(sosulist)
        for j in range(slen):
            if a[i] % a[sosulist[j]] == 0:
                ans = ans - 1
                wkval = 0
                break
            if a[i] // 2 < a[sosulist[j]]:
                break

        if wkval == 1:
            sosulist.append(i)

# Output
print(ans)

Submission status: Wrong Answer

Solution code:
N = int(input())
A = list(set(map(int,input().split())))
B = [True]*len(A)
count = 0
A.sort()
for i in range(len(A)):
    if B[i]:
        count+=1
        for j in range(i+1,len(A)):
            if A[j]%A[i]==0:
                B[j] = False
print(count)

Submission status: Wrong Answer

Solution code:
N = int(input())
A = list(map(int, input().split()))

B = [x for x in set(A) if A.count(x)>1]
A.sort()
s = 0

i = 0

while(i < N-s):
    h = True
    j = 0
    while(j < i and h):
        if A[i]%A[j] == 0:
            a = A.pop(i)
            s += 1
            h = False
        j += 1
    if h:
        i += 1

s += len(B)

print(N-s)

Submission status: Wrong Answer

Solution code:
from math import sqrt
from sys import stdin
input = stdin.readline

n = int(input())
A = list(map(int, input().split()))

A.sort()
ans = 0

div_set = set([])


def div(x):
    for i in range(2, int(sqrt(x)) + 1):
        if x % i == 0:
            if i in div_set or (x // i) in div_set:
                div_set.add(x)
                return False
    div_set.add(x)
    return True


for i in range(n - 1):
    if A[i] in div_set:
        continue
    elif A[i] == A[i + 1]:
        div_set.add(A[i])
        continue
    elif div(A[i]):
        ans += 1

if A[n - 1] not in div_set and div(A[n - 1]):
    ans += 1


print(ans)