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.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.lang.reflect.Array;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.text.DecimalFormat;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Map.Entry;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;

 
 
public class Main {
	public static void main(String[] args) throws IOException{
		  	FastScanner sc = new FastScanner();
			PrintWriter out = new PrintWriter(System.out);
			String str = sc.nextToken();
			String s = sc.nextToken();
			char A[]= str.toCharArray();
			char B[] =s.toCharArray();
			int x[] = new int[B.length];
			for(int i=0;i<B.length;i++){
				x[i]=B[i]-'0';
			}
			for(int i=0;i<x.length/2;i++){
				int tmp = x[i];
				x[i]=x[x.length-i-1];
				x[x.length-i-1]= tmp;
			}
			shuffle(x);
			Arrays.sort(x);
			LinkedList<Integer> L = new LinkedList<Integer>();

			for(int i=0;i<x.length;i++)L.add(x[x.length-i-1]);
			for(int i=0; L.size()>0&&i<A.length;i++){
				int m = L.peek();
				if(m>( A[i]-'0') && L.size()>0)
				{
					A[i]=(char) (L.removeFirst()+'0');
				}
				
			}
			for(char i:A)
				out.print(i);
			out.close();
			
			
			
			
			
			
			
			
	}
	
	
		
	
			
		
	

			

			
			
			
	
	



	
	
			    
			


			
			
	
	
	

			
	
		
	
	
	
		

			

		

	
	

	
	
	

			
						
			

	
	

		
		
		


















































	static void shuffle(int[] a)
	{
		int n = a.length;
		for(int i = 0; i < n; ++i)
		{
			int r = i + (int)(Math.random() * (n - i));
			int tmp = a[r];
			a[r] = a[i];
			a[i] = tmp;
		}
	}


	static void generate(int[] p, int L, int R) {
		  if (L == R) {
		      
		      
		  }else { 
		    for (int i = L; i <= R; i++) {
		    	int tmp = p[L]; p[L] = p[i]; p[i] = tmp;//swap  do
		      generate(p, L+1, R);//recurse 
		      tmp = p[L]; p[L] = p[i]; p[i] = tmp;//unswap  undo

		    }
		  }
		}


















































































































	
}
	 


	class point implements Comparable{
		int x ;int y ;
		point(int x ,int y){
			this.x=x;
			this.y=y;
		}
		@Override
		public int compareTo(Object arg0) {
			// TODO Auto-generated method stub
			point p = (point)arg0;
			if(p.x>this.x)return -1;
			if(p.x<this.x)return 1;
			return 0;
		}
		
	}
	
	
	











	
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
class FastScanner {
 
 
 
 
    BufferedReader br;
    StringTokenizer st;
 
    public FastScanner() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }
 
    public FastScanner(String s) {
        try {
            br = new BufferedReader(new FileReader(s));
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
    }
 
    String nextToken() {
        while (st == null || !st.hasMoreElements()) {
            try {
 
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }
 
    int nextInt() {
        return Integer.parseInt(nextToken());
    }
 
    long nextLong() {
        return Long.parseLong(nextToken());
    }
 
    double nextDouble() {
        return Double.parseDouble(nextToken());
    }
 
 
}