hdu 4002 Find the maximum

Find the maximum

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65768/65768 K (Java/Others)
Total Submission(s): 1561    Accepted Submission(s): 680

Problem Description

Euler's Totient function, φ (n) [sometimes called the phi function], is used to determine the number of numbers less than n which are relatively prime to n . For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and relatively prime to nine, φ(9)=6. 
HG is the master of X Y. One day HG wants to teachers XY something about Euler's Totient function by a mathematic game. That is HG gives a positive integer N and XY tells his master the value of 2<=n<=N for which φ(n) is a maximum. Soon HG finds that this seems a little easy for XY who is a primer of Lupus, because XY gives the right answer very fast by a small program. So HG makes some changes. For this time XY will tells him the value of 2<=n<=N for which n/φ(n) is a maximum. This time XY meets some difficult because he has no enough knowledge to solve this problem. Now he needs your help.

 

Input

There are T test cases (1<=T<=50000). For each test case, standard input contains a line with 2 ≤ n ≤ 10^100.

 

Output

For each test case there should be single line of output answering the question posed above.

 

Sample Input

2
10
100

 

Sample Output

6
30

Hint

If the maximum is achieved more than once, we might pick the smallest such n.

 

Source

The 36th ACM/ICPC Asia Regional Dalian Site —— Online Contest

 import java.io.*;
 import java.awt.*;
 import java.math.BigInteger;
 import java.util.Scanner;

 public class Main {

     static int prime[] = new int [];
     static int len = ;
     static BigInteger dp[] = new BigInteger[];
     public static void main(String[] args) {
         fun();
         int T=;
         Scanner cin  =  new Scanner(System.in);
         T=cin.nextInt();
         while(T>)
         {
             BigInteger n = cin.nextBigInteger();
             int x=;
             for(int i=;i<=len;i++)
             {
                 if(n.compareTo(dp[i])<)
                 {
                     x=i-;
                     break;
                 }
             }
             System.out.println(dp[x]);
             T--;
         }
     }
     static void fun(){
         boolean s[] = new boolean[];
         for(int i=;i<s.length;i++){
             s[i]=false;
         }
         for(int i=;i<dp.length;i++){
             dp[i]=BigInteger.ZERO;
         }
         for(int i=;i<;i++)
         {
             if(s[i]==true) continue;
             prime[++len]=i;
             for(int j=i*;j<;j=j+i)
                 s[j]=true;
         }
         dp[] = BigInteger.ONE;
         for(int i=;i<=len;i++)
         {
             dp[i] = dp[i-].multiply(BigInteger.valueOf(prime[i]));
         }
     }
 }