#include <bits/stdc++.h>
using namespace std;
multiset<int> f;
void addNumber(int j) {
  if (j == 2) {
    f.insert(2);
  } else if (j == 3) {
    f.insert(3);
  } else if (j == 4) {
    f.insert(2);
    f.insert(2);
  } else if (j == 5) {
    f.insert(5);
  } else if (j == 6) {
    f.insert(2);
    f.insert(3);
  } else if (j == 7) {
    f.insert(7);
  } else if (j == 8) {
    f.insert(2);
    f.insert(2);
    f.insert(2);
  } else if (j == 9) {
    f.insert(3);
    f.insert(3);
  }
}
void deleteLastNumber() {
  int v = *(--f.end());
  cout << v;
  for (int i = v; i > 1; --i) {
    if (i == 7) {
      f.erase(f.find(7));
    } else if (i == 6) {
      f.erase(f.find(2));
      f.erase(f.find(3));
    } else if (i == 5) {
      f.erase(f.find(5));
    } else if (i == 4) {
      f.erase(f.find(2));
      f.erase(f.find(2));
    } else if (i == 3) {
      f.erase(f.find(3));
    } else if (i == 2) {
      f.erase(f.find(2));
    }
  }
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n;
  cin >> n;
  string s;
  cin >> s;
  for (int i = 0; i < n; ++i)
    for (int j = 2; j <= int(s[i] - '0'); ++j) addNumber(j);
  while (f.size()) deleteLastNumber();
  cout << "\n";
  return 0;
}

### Prompt

Generate 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;
multiset<int> f;
void addNumber(int j) {
  if (j == 2) {
    f.insert(2);
  } else if (j == 3) {
    f.insert(3);
  } else if (j == 4) {
    f.insert(2);
    f.insert(2);
  } else if (j == 5) {
    f.insert(5);
  } else if (j == 6) {
    f.insert(2);
    f.insert(3);
  } else if (j == 7) {
    f.insert(7);
  } else if (j == 8) {
    f.insert(2);
    f.insert(2);
    f.insert(2);
  } else if (j == 9) {
    f.insert(3);
    f.insert(3);
  }
}
void deleteLastNumber() {
  int v = *(--f.end());
  cout << v;
  for (int i = v; i > 1; --i) {
    if (i == 7) {
      f.erase(f.find(7));
    } else if (i == 6) {
      f.erase(f.find(2));
      f.erase(f.find(3));
    } else if (i == 5) {
      f.erase(f.find(5));
    } else if (i == 4) {
      f.erase(f.find(2));
      f.erase(f.find(2));
    } else if (i == 3) {
      f.erase(f.find(3));
    } else if (i == 2) {
      f.erase(f.find(2));
    }
  }
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n;
  cin >> n;
  string s;
  cin >> s;
  for (int i = 0; i < n; ++i)
    for (int j = 2; j <= int(s[i] - '0'); ++j) addNumber(j);
  while (f.size()) deleteLastNumber();
  cout << "\n";
  return 0;
}

```