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;
char _;
string a;
int i, arr[10], n;
int main() {
  ios::sync_with_stdio(false);
  cin >> n >> a;
  for (i = 0; i < n; ++i) {
    int ch = a[i] - '0';
    if (ch == 4)
      arr[2] += 2, arr[3]++;
    else if (ch == 6)
      arr[5]++, arr[3]++;
    else if (ch == 8)
      arr[7]++, arr[2] += 3;
    else if (ch == 9)
      arr[7]++, arr[2] += 1, arr[3] += 2;
    else
      arr[ch]++;
  }
  for (i = 7; i >= 2; --i) cout << string(arr[i], i + '0');
  cout << endl;
}
