Problem: You are given an integer a that consists of n digits. You are also given a sequence of digits s of length m. The digit in position j (1 ≤ j ≤ m) of sequence s means that you can choose an arbitrary position i (1 ≤ i ≤ n) in a and replace the digit in the chosen position i with sj. Each element in the sequence s can participate in no more than one replacing operation.

Your task is to perform such sequence of replacements, that the given number a gets maximum value. You are allowed to use not all elements from s.

Input

The first line contains positive integer a. Its length n is positive and doesn't exceed 105. The second line contains sequence of digits s. Its length m is positive and doesn't exceed 105. The digits in the sequence s are written consecutively without any separators.

The given number a doesn't contain leading zeroes. 

Output

Print the maximum value that can be obtained from a after a series of replacements. You are allowed to use not all elements from s. The printed number shouldn't contain any leading zeroes.

Examples

Input

1024
010


Output

1124


Input

987
1234567


Output

987

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;

public class Main {
   private static IO io;

   public static void main(String[] args) throws IOException {
       new Main().run();
   }

   private void run() throws IOException {
       io = new IO(System.getProperty("ONLINE_JUDGE")!=null);
       solve();
       io.flush();
   }
   
   private void solve() throws IOException {
       io.wc('0', '9');
       char a[] = io.nS().toCharArray(), s[] = io.nS().toCharArray(); Arrays.sort(s); int j = s.length - 1;
       for(int i = 0; i<a.length&&j>=0; i++)
           if(s[j]>a[i])a[i] = s[j--];
       io.wln(String.valueOf(a));
   }//2.2250738585072012e-308
   
   @SuppressWarnings("unused")
   private class IO{
       StreamTokenizer in; PrintWriter out; BufferedReader br; Reader reader; Writer writer;
       public IO(boolean oj) throws IOException{
           Locale.setDefault(Locale.US);
           reader = oj ? new InputStreamReader(System.in) : new FileReader("input.txt");
           writer = oj ? new OutputStreamWriter(System.out) : new FileWriter("output.txt");
           br = new BufferedReader(reader);
           in = new StreamTokenizer(br);
           out = new PrintWriter(writer);
       }
       public void wln(){out.println();}
       public void wln(int arg){out.println(arg);}
       public void wln(long arg){out.println(arg);}
       public void wln(double arg){out.println(arg);}
       public void wln(String arg){out.println(arg);}
       public void wln(boolean arg){out.println(arg);}
       public void wln(char arg){out.println(arg);}
       public void wln(float arg){out.println(arg);}
       public void wln(Object arg){out.println(arg);}
       public void w(int arg){out.print(arg);}
       public void w(long arg){out.print(arg);}
       public void w(double arg){out.print(arg);}
       public void w(String arg){out.print(arg);}
       public void w(boolean arg){out.print(arg);}
       public void w(char arg){out.print(arg);}
       public void w(float arg){out.print(arg);}
       public void w(Object arg){out.print(arg);}
       public void wf(String format, Object...args){out.printf(format, args);}
       public void flush(){out.flush();}
       public int nI() throws IOException {in.nextToken(); return(int)in.nval;}
       public long nL() throws IOException {in.nextToken(); return(long)in.nval;}
       public String nS() throws IOException {in.nextToken(); return in.sval;}
       public double nD() throws IOException {in.nextToken(); return in.nval;}
       public float nF() throws IOException {in.nextToken(); return (float)in.nval;}
       public void wc(char...a){for(char c : a){in.ordinaryChar(c);in.wordChars(c, c);}}
       public void wc(char c1, char c2){in.ordinaryChars(c1, c2); in.wordChars(c1, c2);}
   }
}