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.awt.Point;
import java.io.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;

import static java.lang.Math.*;

public class Start {

    final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    void init() throws FileNotFoundException {
        if (ONLINE_JUDGE) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        }
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }

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

    public static void mergeSort(int[] a) {
        mergeSort(a, 0, a.length - 1);
    }

    private static void mergeSort(int[] a, int levtIndex, int rightIndex) {
        final int MAGIC_VALUE = 50;
        if (levtIndex < rightIndex) {
            if (rightIndex - levtIndex <= MAGIC_VALUE) {
                insertionSort(a, levtIndex, rightIndex);
            } else {
                int middleIndex = (levtIndex + rightIndex) / 2;
                mergeSort(a, levtIndex, middleIndex);
                mergeSort(a, middleIndex + 1, rightIndex);
                merge(a, levtIndex, middleIndex, rightIndex);
            }
        }
    }

    private static void merge(int[] a, int levtIndex, int middleIndex,
            int rightIndex) {
        int length1 = middleIndex - levtIndex + 1;
        int length2 = rightIndex - middleIndex;
        int[] levtArray = new int[length1];
        int[] rightArray = new int[length2];
        System.arraycopy(a, levtIndex, levtArray, 0, length1);
        System.arraycopy(a, middleIndex + 1, rightArray, 0, length2);
        for (int k = levtIndex, i = 0, j = 0; k <= rightIndex; k++) {
            if (i == length1) {
                a[k] = rightArray[j++];
            } else if (j == length2) {
                a[k] = levtArray[i++];
            } else {
                a[k] = levtArray[i] <= rightArray[j] ? levtArray[i++]
                        : rightArray[j++];
            }
        }
    }

    private static void insertionSort(int[] a, int levtIndex, int rightIndex) {
        for (int i = levtIndex + 1; i <= rightIndex; i++) {
            int current = a[i];
            int j = i - 1;
            while (j >= levtIndex && a[j] > current) {
                a[j + 1] = a[j];
                j--;
            }
            a[j + 1] = current;
        }
    }

    public void run() {
        try {
            long t1 = System.currentTimeMillis();
            init();
            solve();
            out.close();
            long t2 = System.currentTimeMillis();
            System.err.println("Time = " + (t2 - t1));
        } catch (Exception e) {
            e.printStackTrace(System.err);
            System.exit(-1);
        }
    }

    class LoL implements Comparable<LoL> {
        int x;
        int y;

        public LoL(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public int compareTo(LoL arg0) {
            if (arg0.x == x) {
                return y - arg0.y;
            }
            return arg0.x - x;
        }

    }

    public void solve() throws IOException {
        String s = readString();
        String t = readString();
        int n = s.length();
        int m = t.length();
        
        int [] a = new int [n];
        int [] b = new int [m];
        for (int i =0 ; i <n; i++){
            a[i] = s.charAt(i)-'0';
        }
        
        for (int j = 0;  j  < m; j++){
            b[j] = t.charAt(j)-'0';
        }
        mergeSort(b);
        int j = m-1;
        for (int i = 0; i <n; i++){
            if (j>=0){
                if (b[j]>a[i]){
                    a[i] = b[j];
                    j--;
                }
            }
            else{
                break;
            }
        }
        for (int i =0 ; i<n; i++){
            out.print(a[i]);
        }
    }
}