Sphenic numbers（素数筛）

Schoolboy Vasya is interested in the problem of distinguishing prime numbers. He has decided to develop his own testing method for it. Unfortunately, the new algorithm has one deficiency – it yields false positive outputs in case with so-called sphenic numbers. For those who does not know: sphenic number is the product of exactly three distinct prime numbers. Help Vasya write a program to distinguish sphenic numbers.

Inut

The input file contains a single number – integer n.

Limitations

30 ≤ n ≤ 10467397.

Output

The output file must contain one single line with the value “YES” (without quotation marks) if number n is sphenic or “NO” if it is not. Examples

Examples

Input.txt

30

40

10467397 

 

Output.txt

YES

NO

YES

 

 1 #include <stdio.h>
 2 #include <string.h>
 3 #include <math.h>
 4 
 5 #define maxx 10467397/6
 6 
 7 int cur, prime[maxx+10];
 8 int vis[maxx+10];
 9 void find_prime()
10 {
11     int i, j;
12     memset(vis, 0, sizeof(vis));
13     cur = 0;
14     for(i=2; i<maxx; i++)
15     {
16         if(vis[i]==0)
17         {
18             prime[cur++] = i;
19             for(j=1; j*i<=maxx; j++)
20             {
21                 vis[j*i] = 1;
22             }
23         }
24 
25     }
26 }
27 
28 int solve(int n)
29 {
30     int num = 0, i;
31     for(i=0; i<cur&&n>1; i++)
32     {
33         if(n % prime[i]==0)
34         {
35             num++;
36             n/=prime[i];
37         }
38         if(n % prime[i]==0) break;
39     }  
40     if(num==3&&n==1&&!(i<cur&&n>1)) return 1;
41     else return 0;
42 }
43 
44 int main()
45 {
46     freopen("input.txt", "r", stdin);
47     freopen("output.txt", "w", stdout);
48     int n;
49     find_prime();
50     scanf("%d", &n);
51     if(solve(n)) printf("YES\n");
52     else printf("NO\n");
53     return 0;
54 }

 

posted @ 2019-08-12 20:53  Xxiaoyu  阅读(156)  评论(0)  编辑  收藏  举报