Codeforces--630K--Indivisibility（容斥）



K -
Indivisibility

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Time Limit:500MS    
Memory Limit:65536KB     64bit IO Format:%I64d & %I64u

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Description

IT City company developing computer games decided to upgrade its way to reward its employees. Now it looks the following way. After a new game release users start buying it actively, and the company tracks the number of sales with precision to each transaction.
Every time when the next number of sales is not divisible by any number from
2 to 10 every developer of this game gets a small bonus.

A game designer Petya knows that the company is just about to release a new game that was partly developed by him. On the basis of his experience he predicts that
n people will buy the game during the first month. Now Petya wants to determine how many times he will get the bonus. Help him to know it.

Input

The only line of the input contains one integer n (1 ≤ n ≤ 10¹⁸) — the prediction on the number of people who
will buy the game.

Output

Output one integer showing how many numbers from 1 to
n are not divisible by any number from
2 to 10.

Sample Input

Input

12

Output

2

求1--n之间有多少个数可以不被2--10中的任何一个数整除，首先2--10中的数可以由2，3，5，7中的几个数组合表示，所以n/2+n/3+n/5+n/7包含需要的所有的数，但是其中也有重合的部分，比如12是2,3，的倍数，所以需要从2,3,5,7中任取2--4个数进行组合，去除重复的

#include<iostream>
using namespace std;
int main()
{
	__int64 n;
	while(cin>>n)
	{
		__int64 m=n/2+n/3+n/5+n/7-n/6-n/10-n/14-n/15
		-n/21-n/35+n/30+n/70+n/42+n/105-n/210;
        m=n-m;
        cout<<m<<endl;
	}
	return 0;
}