#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:66777216")
using namespace std;
int DG(int x, int n) {
  int cr = x;
  int res = 0;
  while (cr <= n) {
    res += n / cr;
    cr *= x;
  }
  return res;
}
int q[10];
int q2[10];
char c[100];
void solve() {
  int n;
  scanf("%d", &n);
  scanf("%s", &c);
  vector<int> pr;
  pr.push_back(2);
  pr.push_back(3);
  pr.push_back(5);
  pr.push_back(7);
  for (int i = 0; i < (int)(n); ++i) {
    if (c[i] >= '0') {
      for (int j = 0; j < (int)(((int)((pr).size()))); ++j)
        q[pr[j]] += DG(pr[j], c[i] - '0');
    }
  }
  for (int i = 0; i < (int)(10); ++i) q2[i] = q[i];
  vector<int> res;
  for (int i = (int)(((int)((pr).size()))) - 1; i >= 0; --i) {
    int t = pr[i];
    if (q2[t]) {
      for (int j = (int)(i)-1; j >= 0; --j) q2[pr[j]] -= q2[t] * DG(pr[j], t);
      for (int u = 0; u < (int)(q2[t]); ++u) res.push_back(pr[i]);
      q2[t] = 0;
    }
  }
  for (int i = 0; i < (int)(((int)((res).size()))); ++i) printf("%d", res[i]);
  puts("");
}
void testgen() {
  FILE* file_ = fopen("input.txt", "w");
  fclose(file_);
}
int main() {
  cout << fixed;
  cout.precision(15);
  cerr << fixed;
  cerr.precision(12);
  solve();
  return 0;
}

### Prompt

Please create a solution in cpp to the following problem:

Drazil is playing a math game with Varda.

Let's define <image> for positive integer x as a product of factorials of its digits. For example, <image>.

First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions:

1. x doesn't contain neither digit 0 nor digit 1.

2. <image> = <image>.

Help friends find such number.

Input

The first line contains an integer n (1 ≤ n ≤ 15) — the number of digits in a.

The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes.

Output

Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation.

Examples

Input

4
1234


Output

33222


Input

3
555


Output

555

Note

In the first case, <image>

### Response

```cpp
#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:66777216")
using namespace std;
int DG(int x, int n) {
  int cr = x;
  int res = 0;
  while (cr <= n) {
    res += n / cr;
    cr *= x;
  }
  return res;
}
int q[10];
int q2[10];
char c[100];
void solve() {
  int n;
  scanf("%d", &n);
  scanf("%s", &c);
  vector<int> pr;
  pr.push_back(2);
  pr.push_back(3);
  pr.push_back(5);
  pr.push_back(7);
  for (int i = 0; i < (int)(n); ++i) {
    if (c[i] >= '0') {
      for (int j = 0; j < (int)(((int)((pr).size()))); ++j)
        q[pr[j]] += DG(pr[j], c[i] - '0');
    }
  }
  for (int i = 0; i < (int)(10); ++i) q2[i] = q[i];
  vector<int> res;
  for (int i = (int)(((int)((pr).size()))) - 1; i >= 0; --i) {
    int t = pr[i];
    if (q2[t]) {
      for (int j = (int)(i)-1; j >= 0; --j) q2[pr[j]] -= q2[t] * DG(pr[j], t);
      for (int u = 0; u < (int)(q2[t]); ++u) res.push_back(pr[i]);
      q2[t] = 0;
    }
  }
  for (int i = 0; i < (int)(((int)((res).size()))); ++i) printf("%d", res[i]);
  puts("");
}
void testgen() {
  FILE* file_ = fopen("input.txt", "w");
  fclose(file_);
}
int main() {
  cout << fixed;
  cout.precision(15);
  cerr << fixed;
  cerr.precision(12);
  solve();
  return 0;
}

```