CodeForces - 757B Bash's Big Day (分解素因子)

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题意：

给出 N 个数，从中挑选几个数，要求每个数的 gcd 不等于 1 ，问满足条件的数集最大有几个数？

思路：

将每个数进行素数分解，统计素数出现的次数，素数中出现最多次的，就是所求最大数集的 gcd ，答案就是它出现次数。

注意到数字1的特殊性，所以在统计时略去。

代码：

#include <bits/stdc++.h>using namespace std;const int MAXN=1e5;bool prime[MAXN+1000];int n,cut[MAXN+1000],x,a[MAXN+1000][15];//...........................a 用于保存素因子，对于每个小于1e5的数，它的素因子不会超15种void getP(){                               memset(prime,0,sizeof(prime));    memset(a,0,sizeof(a));    prime[0]=prime[1]=1;    for(int i=2;i<=MAXN;i++){//......................................类似素数筛的写法，筛选出每个数的素因子        a[i][++a[i][0]]=i;        if(!prime[i]){            for(int j=2;j*i<=MAXN;j++){                prime[j*i]=1;                a[j*i][++a[j*i][0]]=i;            }        }    }}void cont(){//.......................................................统计每个素因子出现次数    for(int i=1;i<=a[x][0];i++)        cut[a[x][i]]++;}int main(){    getP();    ios::sync_with_stdio(false);    while(scanf("%d",&n)!=-1){        memset(cut,0,sizeof(cut));        for(int i=0;i<n;i++){            scanf("%d",&x);            cont();        }        cout<<max(1,*max_element(cut,cut+MAXN+10))<<endl;//...........考虑到只有一个1的情况    }}

Bash has set out on a journey to become the greatest Pokemon master. To get his first Pokemon, he went to Professor Zulu's Lab. Since Bash is Professor Zulu's favourite student, Zulu allows him to take as many Pokemon from his lab as he pleases.

But Zulu warns him that a group of k > 1 Pokemon with strengths {s1, s2, s3, ..., sk} tend to fight among each other ifgcd(s1, s2, s3, ..., sk) = 1 (see notes for gcd definition).

Bash, being smart, does not want his Pokemon to fight among each other. However, he also wants to maximize the number of Pokemon he takes from the lab. Can you help Bash find out the maximum number of Pokemon he can take?

Note: A Pokemon cannot fight with itself.

Input

The input consists of two lines.

The first line contains an integer n (1 ≤ n ≤ 105), the number of Pokemon in the lab.

The next line contains n space separated integers, where the i-th of them denotes si (1 ≤ si ≤ 105), the strength of the i-th Pokemon.

Output

Print single integer — the maximum number of Pokemons Bash can take.

Examples
input
32 3 4
output
2
input
52 3 4 6 7
output
3

Note

gcd (greatest common divisor) of positive integers set {a1, a2, ..., an} is the maximum positive integer that divides all the integers{a1, a2, ..., an}.

In the first sample, we can take Pokemons with strengths {2, 4} since gcd(2, 4) = 2.

In the second sample, we can take Pokemons with strengths {2, 4, 6}, and there is no larger group with gcd ≠ 1.

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