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() {
  vector<string> a(9);
  a[0] = "1", a[1] = "2", a[2] = "3", a[3] = "322", a[4] = "5", a[5] = "53",
  a[6] = "7", a[7] = "7222", a[8] = "7332";
  long long int n;
  cin >> n;
  string s;
  cin >> s;
  string p = "";
  for (long long int i = 0; i < n; i++) {
    if (s[i] - '1' == 0) continue;
    p += a[s[i] - '1'];
  }
  sort(p.begin(), p.end());
  reverse(p.begin(), p.end());
  cout << p << "\n";
}
