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 main() {
  int n;
  cin >> n;
  int cnt[10] = {0};
  while (n--) {
    char c;
    cin >> c;
    switch (c - '0') {
      case 4:
        cnt[2] += 2;
        cnt[3]++;
        break;
      case 6:
        cnt[3]++;
        cnt[5]++;
        break;
      case 8:
        cnt[2] += 3;
        cnt[7]++;
        break;
      case 9:
        cnt[3] += 2;
        cnt[2]++;
        cnt[7]++;
        break;
      default:
        cnt[c - '0']++;
    }
  }
  for (int i = 9; i > 1; i--) {
    if (cnt[i])
      for (int j = 0; j < cnt[i]; j++) cout << i;
  }
  return 0;
}
