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>
#include <bits/stdc++.h>
using namespace std;
int d[15];
int main() {
  int n;
  scanf("%d", &n);
  char s[20];
  scanf("%s", s);
  vector<int> pm = {2, 3, 5, 7};
  for (int i = 0; i < (int)(n); ++i) {
    int u = s[i] - '0';
    for (int k = (int)(2); k <= (int)(u); ++k) {
      int t = k;
      for (int p : pm)
        while (t % p == 0) ++d[p], t /= p;
    }
  }
  string res;
  for (int i = (int)(3); i >= (int)(0); --i) {
    int p = pm[i];
    for (int j = 0; j < (int)(d[p]); ++j) res += '0' + p;
    int o = d[p];
    for (int ss = 0; ss < (int)(o); ++ss)
      for (int j = (int)(2); j <= (int)(p); ++j) {
        int t = j;
        for (int k : pm)
          while (t % k == 0) --d[k], t /= k;
      }
  }
  puts(res.c_str());
  return 0;
}
