#include <bits/stdc++.h>
using namespace std;
int main() {
  int n;
  cin >> n;
  string num;
  cin >> num;
  map<int, int> factors;
  vector<int> all_f;
  for (int bn = 0; bn < num.length(); bn++) {
    for (int tt = num[bn] - '0'; tt >= 2; tt--) {
      int t = tt;
      while (t > 1) {
        for (int i = 2; i <= t; i++) {
          if (t % i == 0) {
            if (factors.count(i)) {
              factors[i]++;
            } else {
              factors[i] = 1;
              all_f.push_back(i);
            }
            t /= i;
            break;
          }
        }
      }
    }
  }
  vector<int> ans;
  sort(all_f.begin(), all_f.end(), greater<int>());
  for (auto it = all_f.begin(); it != all_f.end(); it++) {
    if (factors[*it]) {
      for (int i = 0; i < factors[*it]; i++) {
        ans.push_back(*it);
        for (int j = *it - 1; j >= 2; j--) {
          int yo = j;
          while (yo > 1) {
            for (int y = 2; y <= yo; y++) {
              if (yo % y == 0) {
                factors[y]--;
                yo /= y;
              }
            }
          }
        }
      }
    }
  }
  for (auto it = ans.begin(); it != ans.end(); it++) {
    cout << *it;
  }
}

### Prompt

Please formulate a Cpp solution 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>
using namespace std;
int main() {
  int n;
  cin >> n;
  string num;
  cin >> num;
  map<int, int> factors;
  vector<int> all_f;
  for (int bn = 0; bn < num.length(); bn++) {
    for (int tt = num[bn] - '0'; tt >= 2; tt--) {
      int t = tt;
      while (t > 1) {
        for (int i = 2; i <= t; i++) {
          if (t % i == 0) {
            if (factors.count(i)) {
              factors[i]++;
            } else {
              factors[i] = 1;
              all_f.push_back(i);
            }
            t /= i;
            break;
          }
        }
      }
    }
  }
  vector<int> ans;
  sort(all_f.begin(), all_f.end(), greater<int>());
  for (auto it = all_f.begin(); it != all_f.end(); it++) {
    if (factors[*it]) {
      for (int i = 0; i < factors[*it]; i++) {
        ans.push_back(*it);
        for (int j = *it - 1; j >= 2; j--) {
          int yo = j;
          while (yo > 1) {
            for (int y = 2; y <= yo; y++) {
              if (yo % y == 0) {
                factors[y]--;
                yo /= y;
              }
            }
          }
        }
      }
    }
  }
  for (auto it = ans.begin(); it != ans.end(); it++) {
    cout << *it;
  }
}

```