#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
using namespace std;
const int mod = 1000000007;
mt19937 rng((int)std::chrono::steady_clock::now().time_since_epoch().count());
class segment_tree {
 public:
  long long rmaxq[4 * 100000], rminq[4 * 100000], rsumq[4 * 100000];
  void init() {
    for (int i = 0; i < 4 * 100000; i++) {
      rmaxq[i] = 0;
      rminq[i] = 0;
      rsumq[i] = 0;
    }
  }
  void upd_rminq(int lb, int rb, int tar, int ok, long long val) {
    if (lb == rb) {
      rminq[ok] = val;
      return;
    }
    int mid = (lb + rb) / 2;
    if (tar <= mid) {
      upd_rminq(lb, mid, tar, 2 * ok + 1, val);
    } else {
      upd_rminq(mid + 1, rb, tar, 2 * ok + 2, val);
    }
    rminq[ok] = min(rminq[2 * ok + 1], rminq[2 * ok + 2]);
  }
  long long query_rminq(int lb, int rb, int ok, int lconst, int rconst) {
    if (rconst < lb || lconst > rb) {
      return LLONG_MAX;
    }
    if (lconst <= lb && rb <= rconst) {
      return rminq[ok];
    }
    int mid = (lb + rb) / 2;
    return min(query_rminq(lb, mid, ok * 2 + 1, lconst, rconst),
               query_rminq(mid + 1, rb, ok * 2 + 2, lconst, rconst));
  }
  void updall_rminq(long long arr[], int n) {
    for (int i = 0; i < n; i++) upd_rminq(0, 100000 - 1, i, 0, arr[i]);
  }
  void upd_rmaxq(int lb, int rb, int tar, int ok, long long val) {
    if (lb == rb) {
      rmaxq[ok] = val;
      return;
    }
    int mid = (lb + rb) / 2;
    if (tar <= mid) {
      upd_rmaxq(lb, mid, tar, 2 * ok + 1, val);
    } else {
      upd_rmaxq(mid + 1, rb, tar, 2 * ok + 2, val);
    }
    rmaxq[ok] = max(rmaxq[2 * ok + 1], rmaxq[2 * ok + 2]);
  }
  long long query_rmaxq(int lb, int rb, int ok, int lconst, int rconst) {
    if (rconst < lb || lconst > rb) {
      return LLONG_MIN;
    }
    if (lconst <= lb && rb <= rconst) {
      return rmaxq[ok];
    }
    int mid = (lb + rb) / 2;
    return max(query_rmaxq(lb, mid, ok * 2 + 1, lconst, rconst),
               query_rmaxq(mid + 1, rb, ok * 2 + 2, lconst, rconst));
  }
  void updall_rmaxq(long long arr[], int n) {
    for (int i = 0; i < n; i++) {
      upd_rmaxq(0, 100000 - 1, i, 0, arr[i]);
    }
  }
  void upd_rsumq(int lb, int rb, int tar, int ok, long long val) {
    if (lb == rb) {
      rsumq[ok] = val;
      return;
    }
    int mid = (lb + rb) / 2;
    if (tar <= mid) {
      upd_rsumq(lb, mid, tar, 2 * ok + 1, val);
    } else {
      upd_rsumq(mid + 1, rb, tar, 2 * ok + 2, val);
    }
    rsumq[ok] = rsumq[2 * ok + 1] + rsumq[2 * ok + 2];
  }
  long long query_rsumq(int lb, int rb, int ok, int lconst, int rconst) {
    if (rconst < lb || lconst > rb) {
      return 0;
    }
    if (lconst <= lb && rb <= rconst) {
      return rsumq[ok];
    }
    int mid = (lb + rb) / 2;
    return query_rsumq(lb, mid, ok * 2 + 1, lconst, rconst) +
           query_rsumq(mid + 1, rb, ok * 2 + 2, lconst, rconst);
  }
  void updall_rsumq(long long arr[], int n) {
    for (int i = 0; i < n; i++) upd_rsumq(0, 100000 - 1, i, 0, arr[i]);
  }
} st;
class set_union {
 public:
  int a[100000 + 1];
  void init() {
    for (int i = 0; i <= 100000; i++) a[i] = i;
  }
  int set_of(int u) {
    if (a[u] == u)
      return u;
    else
      return a[u] = set_of(a[u]);
  }
  void union_(int u, int v) { a[set_of(u)] = set_of(v); }
  struct SEGT {
    int index;
    char type;
  };
  SEGT make_SEGT(int a, char b) {
    SEGT esgewqt = {a, b};
    return esgewqt;
  }
  class SEGT_COMP {
   public:
    bool operator()(SEGT a, SEGT b) {
      if (a.index == b.index)
        return a.type < b.type;
      else
        return a.index > b.index;
    }
  };
  vector<pair<int, int> > segment_union(vector<pair<int, int> > V, int T) {
    for (int i = 0; i < V.size(); i++) {
      if (V[i].first > V[i].second) {
        swap(V[i].first, V[i].second);
      }
    }
    priority_queue<SEGT, vector<SEGT>, SEGT_COMP> segt_pq1;
    for (int i = 0; i < V.size(); i++) {
      segt_pq1.push(make_SEGT(V[i].first - T, 'S'));
      segt_pq1.push(make_SEGT(V[i].second, 'E'));
    }
    stack<SEGT> process;
    vector<pair<int, int> > UwU;
    while (segt_pq1.size()) {
      if (segt_pq1.top().type == 'E') {
        process.pop();
        if (process.size() == 0) {
          UwU[int(UwU.size()) - 1].second = segt_pq1.top().index;
        }
      } else {
        process.push(segt_pq1.top());
        if (process.size() == 1) {
          UwU.push_back({segt_pq1.top().index + T, 0});
        }
      }
      segt_pq1.pop();
    }
    return UwU;
  }
} su;
void include() {}
void solve() {
  string a;
  cin >> a;
  string s;
  cin >> s;
  sort(s.begin(), s.end());
  int S = s.size();
  int pointer = S - 1;
  int A = a.size();
  for (int i = 0; i < A; i++) {
    if (a[i] < s[pointer]) {
      a[i] = s[pointer];
      pointer--;
    }
  }
  cout << a;
}
int main() {
  srand(time(NULL));
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  include();
  int t = 1;
  while (t--) {
    solve();
  }
}

### Prompt

Your task is to create a CPP solution to the following 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

### Response

```cpp
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
using namespace std;
const int mod = 1000000007;
mt19937 rng((int)std::chrono::steady_clock::now().time_since_epoch().count());
class segment_tree {
 public:
  long long rmaxq[4 * 100000], rminq[4 * 100000], rsumq[4 * 100000];
  void init() {
    for (int i = 0; i < 4 * 100000; i++) {
      rmaxq[i] = 0;
      rminq[i] = 0;
      rsumq[i] = 0;
    }
  }
  void upd_rminq(int lb, int rb, int tar, int ok, long long val) {
    if (lb == rb) {
      rminq[ok] = val;
      return;
    }
    int mid = (lb + rb) / 2;
    if (tar <= mid) {
      upd_rminq(lb, mid, tar, 2 * ok + 1, val);
    } else {
      upd_rminq(mid + 1, rb, tar, 2 * ok + 2, val);
    }
    rminq[ok] = min(rminq[2 * ok + 1], rminq[2 * ok + 2]);
  }
  long long query_rminq(int lb, int rb, int ok, int lconst, int rconst) {
    if (rconst < lb || lconst > rb) {
      return LLONG_MAX;
    }
    if (lconst <= lb && rb <= rconst) {
      return rminq[ok];
    }
    int mid = (lb + rb) / 2;
    return min(query_rminq(lb, mid, ok * 2 + 1, lconst, rconst),
               query_rminq(mid + 1, rb, ok * 2 + 2, lconst, rconst));
  }
  void updall_rminq(long long arr[], int n) {
    for (int i = 0; i < n; i++) upd_rminq(0, 100000 - 1, i, 0, arr[i]);
  }
  void upd_rmaxq(int lb, int rb, int tar, int ok, long long val) {
    if (lb == rb) {
      rmaxq[ok] = val;
      return;
    }
    int mid = (lb + rb) / 2;
    if (tar <= mid) {
      upd_rmaxq(lb, mid, tar, 2 * ok + 1, val);
    } else {
      upd_rmaxq(mid + 1, rb, tar, 2 * ok + 2, val);
    }
    rmaxq[ok] = max(rmaxq[2 * ok + 1], rmaxq[2 * ok + 2]);
  }
  long long query_rmaxq(int lb, int rb, int ok, int lconst, int rconst) {
    if (rconst < lb || lconst > rb) {
      return LLONG_MIN;
    }
    if (lconst <= lb && rb <= rconst) {
      return rmaxq[ok];
    }
    int mid = (lb + rb) / 2;
    return max(query_rmaxq(lb, mid, ok * 2 + 1, lconst, rconst),
               query_rmaxq(mid + 1, rb, ok * 2 + 2, lconst, rconst));
  }
  void updall_rmaxq(long long arr[], int n) {
    for (int i = 0; i < n; i++) {
      upd_rmaxq(0, 100000 - 1, i, 0, arr[i]);
    }
  }
  void upd_rsumq(int lb, int rb, int tar, int ok, long long val) {
    if (lb == rb) {
      rsumq[ok] = val;
      return;
    }
    int mid = (lb + rb) / 2;
    if (tar <= mid) {
      upd_rsumq(lb, mid, tar, 2 * ok + 1, val);
    } else {
      upd_rsumq(mid + 1, rb, tar, 2 * ok + 2, val);
    }
    rsumq[ok] = rsumq[2 * ok + 1] + rsumq[2 * ok + 2];
  }
  long long query_rsumq(int lb, int rb, int ok, int lconst, int rconst) {
    if (rconst < lb || lconst > rb) {
      return 0;
    }
    if (lconst <= lb && rb <= rconst) {
      return rsumq[ok];
    }
    int mid = (lb + rb) / 2;
    return query_rsumq(lb, mid, ok * 2 + 1, lconst, rconst) +
           query_rsumq(mid + 1, rb, ok * 2 + 2, lconst, rconst);
  }
  void updall_rsumq(long long arr[], int n) {
    for (int i = 0; i < n; i++) upd_rsumq(0, 100000 - 1, i, 0, arr[i]);
  }
} st;
class set_union {
 public:
  int a[100000 + 1];
  void init() {
    for (int i = 0; i <= 100000; i++) a[i] = i;
  }
  int set_of(int u) {
    if (a[u] == u)
      return u;
    else
      return a[u] = set_of(a[u]);
  }
  void union_(int u, int v) { a[set_of(u)] = set_of(v); }
  struct SEGT {
    int index;
    char type;
  };
  SEGT make_SEGT(int a, char b) {
    SEGT esgewqt = {a, b};
    return esgewqt;
  }
  class SEGT_COMP {
   public:
    bool operator()(SEGT a, SEGT b) {
      if (a.index == b.index)
        return a.type < b.type;
      else
        return a.index > b.index;
    }
  };
  vector<pair<int, int> > segment_union(vector<pair<int, int> > V, int T) {
    for (int i = 0; i < V.size(); i++) {
      if (V[i].first > V[i].second) {
        swap(V[i].first, V[i].second);
      }
    }
    priority_queue<SEGT, vector<SEGT>, SEGT_COMP> segt_pq1;
    for (int i = 0; i < V.size(); i++) {
      segt_pq1.push(make_SEGT(V[i].first - T, 'S'));
      segt_pq1.push(make_SEGT(V[i].second, 'E'));
    }
    stack<SEGT> process;
    vector<pair<int, int> > UwU;
    while (segt_pq1.size()) {
      if (segt_pq1.top().type == 'E') {
        process.pop();
        if (process.size() == 0) {
          UwU[int(UwU.size()) - 1].second = segt_pq1.top().index;
        }
      } else {
        process.push(segt_pq1.top());
        if (process.size() == 1) {
          UwU.push_back({segt_pq1.top().index + T, 0});
        }
      }
      segt_pq1.pop();
    }
    return UwU;
  }
} su;
void include() {}
void solve() {
  string a;
  cin >> a;
  string s;
  cin >> s;
  sort(s.begin(), s.end());
  int S = s.size();
  int pointer = S - 1;
  int A = a.size();
  for (int i = 0; i < A; i++) {
    if (a[i] < s[pointer]) {
      a[i] = s[pointer];
      pointer--;
    }
  }
  cout << a;
}
int main() {
  srand(time(NULL));
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  include();
  int t = 1;
  while (t--) {
    solve();
  }
}

```