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;
vector<vector<int>> facs = {{},  {},     {2}, {3},       {2, 2},
                            {5}, {2, 3}, {7}, {2, 2, 2}, {3, 3}};
vector<int> primes = {7, 5, 3, 2};
int nums[10];
int main() {
  int n;
  scanf("%d", &n);
  char s[20];
  scanf("%s", s);
  for (int i = 0; i < n; i++)
    for (int j = 2; j <= s[i] - '0'; j++)
      for (auto p : facs[j]) nums[p]++;
  for (auto p : primes)
    for (int i = 0; i < nums[p];) {
      for (int j = 2; j <= p; j++)
        for (auto x : facs[j]) nums[x]--;
      printf("%d", p);
    }
  return 0;
}
