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;
  scanf("%d\n", &n);
  string s;
  getline(cin, s);
  vector<int> a(10);
  for (char i : s)
    if (i == '2') {
      a[2]++;
    } else if (i == '3') {
      a[3]++;
    } else if (i == '4') {
      a[2] += 2;
      a[3]++;
    } else if (i == '5') {
      a[5]++;
    } else if (i == '6') {
      a[3]++;
      a[5]++;
    } else if (i == '7') {
      a[7]++;
    } else if (i == '8') {
      a[7]++;
      a[2] += 3;
    } else if (i == '9') {
      a[3] += 2;
      a[2]++;
      a[7]++;
    }
  for (int num = 9; num > 1; num--)
    while (a[num]--) {
      printf("%d", num);
    }
  return 0;
}
