Problem:
Prime Factorization

Factorize a given integer n.

Input

n

An integer n is given in a line.

Output

Print the given integer n and :. Then, print prime factors in ascending order. If n is divisible by a prime factor several times, the prime factor should be printed according to the number of times. Print a space before each prime factor.

Constraints

2 ≤ n ≤ 109

Sample Input 1

12

Sample Output 1

12: 2 2 3

Sample Input 2

126

Sample Output 2

126: 2 3 3 7

Solution in JAVA (judge verdict: Time Limit Exceeded)

import java.io.InputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Comparator;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.Map;
import java.util.NoSuchElementException;
import java.util.PriorityQueue;
import java.util.TreeMap;
import java.math.BigDecimal;
import java.math.BigInteger;
    
public class Main{
 
static final InputStream in=System.in;
static final PrintWriter out=new PrintWriter(System.out);
static final int INF=Integer.MAX_VALUE;
static final long LINF=Long.MAX_VALUE;
static boolean[] p;
 
public static void main(String[] args) throws IOException{
InputReader ir=new InputReader(in);
int n=ir.nextInt();
p=sieveOfEratosthenes(n);
out.println(n+":"+factorize(n));
out.flush();
}

public static String factorize(int n){
 if(p[n]) return " "+Integer.toString(n);
 int t=2;
 StringBuilder sb=new StringBuilder();
 while(true){
  if(p[t]&&n%t==0){
   sb.append(" ");
   sb.append(Integer.toString(t));
   sb.append(factorize(n/t));
   break;
  }
  else t++;
 }
 return sb.toString();
}

public static boolean[] sieveOfEratosthenes(int n){
 boolean[] res=new boolean[n+1];
 Arrays.fill(res,true);
 res[0]=res[1]=false;
 for(int i=2;i<=Math.sqrt(n);i++){
  if(res[i]){
   for(int j=i+i;j<=n;j+=i){
    res[j]=false;
   }
  }
 }
 return res;
}

static class InputReader {
 private InputStream in;
 private byte[] buffer=new byte[1024];
 private int curbuf;
 private int lenbuf;
 
 public InputReader(InputStream in) {this.in=in; this.curbuf=this.lenbuf=0;}
  
 public boolean hasNextByte() {
  if(curbuf>=lenbuf){
   curbuf= 0;
   try{
    lenbuf=in.read(buffer);
   }catch(IOException e) {
    throw new InputMismatchException();
   }
   if(lenbuf<=0) return false;
  }
  return true;
 }
 
 private int readByte(){if(hasNextByte()) return buffer[curbuf++]; else return -1;}

 private boolean isSpaceChar(int c){return !(c>=33&&c<=126);}
 
 private void skip(){while(hasNextByte()&&isSpaceChar(buffer[curbuf])) curbuf++;}

 public boolean hasNext(){skip(); return hasNextByte();}
 
 public String next(){
  if(!hasNext()) throw new NoSuchElementException();
  StringBuilder sb=new StringBuilder();
  int b=readByte();
  while(!isSpaceChar(b)){
   sb.appendCodePoint(b);
   b=readByte();
  }
  return sb.toString();
 }
 
 public int nextInt() {
  if(!hasNext()) throw new NoSuchElementException();
  int c=readByte();
  while (isSpaceChar(c)) c=readByte();
  boolean minus=false;
  if (c=='-') {
   minus=true;
   c=readByte();
  }
  int res=0;
  do{
   if(c<'0'||c>'9') throw new InputMismatchException();
   res=res*10+c-'0';
   c=readByte();
  }while(!isSpaceChar(c));
  return (minus)?-res:res;
 }
 
 public long nextLong() {
  if(!hasNext()) throw new NoSuchElementException();
  int c=readByte();
  while (isSpaceChar(c)) c=readByte();
  boolean minus=false;
  if (c=='-') {
   minus=true;
   c=readByte();
  }
  long res = 0;
  do{
   if(c<'0'||c>'9') throw new InputMismatchException();
   res=res*10+c-'0';
   c=readByte();
  }while(!isSpaceChar(c));
  return (minus)?-res:res;
 }
 
 public double nextDouble(){return Double.parseDouble(next());}
 
 public BigInteger nextBigInteger(){return new BigInteger(next());}
 
 public int[] nextIntArray(int n){
  int[] a=new int[n];
  for(int i=0;i<n;i++) a[i]=nextInt();
  return a;
 }
 
 public char[][] nextCharMap(int n,int m){
  char[][] map=new char[n][m];
  for(int i=0;i<n;i++) map[i]=next().toCharArray();
  return map;
 }
}
}