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 N;
vector<vector<int>> factors = {{1}, {1},    {2}, {3},          {2, 2, 3},
                               {5}, {3, 5}, {7}, {2, 2, 2, 7}, {7, 2, 3, 3}};
int main() {
  cin >> N;
  cin.get();
  vector<int> res;
  for (int i = 0; i < N; i++) {
    int digit = cin.get() - '0';
    for (int factor : factors[digit]) {
      res.push_back(factor);
    }
  }
  sort(res.begin(), res.end(), [](int a, int b) -> bool { return a > b; });
  for (int i : res)
    if (i > 1) cout << i;
  return 0;
}
