#include <bits/stdc++.h>
using namespace std;
const int maxN = 30;
int n;
char str[maxN];
int d[maxN];
void gao(int x) {
  for (; x >= 2; x--) {
    if (x == 2)
      d[2]--;
    else if (x == 3)
      d[3]--;
    else if (x == 4)
      d[2]--, d[2]--;
    else if (x == 5)
      d[5]--;
    else if (x == 6)
      d[2]--, d[3]--;
    else if (x == 7)
      d[7]--;
    else if (x == 8)
      d[2]--, d[2]--, d[2]--;
    else if (x == 9)
      d[3]--, d[3]--;
  }
}
int main() {
  cin >> n >> str;
  memset(d, 0, sizeof(d));
  for (int i = 0; i < n; i++) {
    int x = str[i] - '0';
    while (x >= 2) {
      if (x == 2)
        d[2]++;
      else if (x == 3)
        d[3]++;
      else if (x == 4)
        d[2]++, d[2]++;
      else if (x == 5)
        d[5]++;
      else if (x == 6)
        d[2]++, d[3]++;
      else if (x == 7)
        d[7]++;
      else if (x == 8)
        d[2]++, d[2]++, d[2]++;
      else if (x == 9)
        d[3]++, d[3]++;
      x--;
    }
  }
  for (int x = 9; x >= 2; x--) {
    while (d[x] > 0) {
      d[x]--;
      cout << x;
      gao(x - 1);
    }
  }
  cout << endl;
  return 0;
}

### Prompt

Your challenge is to write 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;
const int maxN = 30;
int n;
char str[maxN];
int d[maxN];
void gao(int x) {
  for (; x >= 2; x--) {
    if (x == 2)
      d[2]--;
    else if (x == 3)
      d[3]--;
    else if (x == 4)
      d[2]--, d[2]--;
    else if (x == 5)
      d[5]--;
    else if (x == 6)
      d[2]--, d[3]--;
    else if (x == 7)
      d[7]--;
    else if (x == 8)
      d[2]--, d[2]--, d[2]--;
    else if (x == 9)
      d[3]--, d[3]--;
  }
}
int main() {
  cin >> n >> str;
  memset(d, 0, sizeof(d));
  for (int i = 0; i < n; i++) {
    int x = str[i] - '0';
    while (x >= 2) {
      if (x == 2)
        d[2]++;
      else if (x == 3)
        d[3]++;
      else if (x == 4)
        d[2]++, d[2]++;
      else if (x == 5)
        d[5]++;
      else if (x == 6)
        d[2]++, d[3]++;
      else if (x == 7)
        d[7]++;
      else if (x == 8)
        d[2]++, d[2]++, d[2]++;
      else if (x == 9)
        d[3]++, d[3]++;
      x--;
    }
  }
  for (int x = 9; x >= 2; x--) {
    while (d[x] > 0) {
      d[x]--;
      cout << x;
      gao(x - 1);
    }
  }
  cout << endl;
  return 0;
}

```