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 prime[11][4];
int primes[4] = {2, 3, 5, 7};
int main() {
  for (int i = 1; i <= 9; i++) {
    for (int j = 0; j < 4; j++) {
      int temp = 0;
      long long temp2 = i;
      for (long long k = i - 1; k >= 1; k--) temp2 *= k;
      while (temp2 % primes[j] == 0) {
        temp++;
        temp2 /= primes[j];
      }
      prime[i][j] = temp;
    }
  }
  int temp23[4] = {0};
  int n;
  cin >> n;
  string s;
  cin >> s;
  for (int i = 0; i < n; i++) {
    int tempo = s[i] - '0';
    for (int j = 0; j < 4; j++) temp23[j] += prime[tempo][j];
  }
  int ans[4] = {0};
  for (int i = 3; i >= 0; i--) {
    while (temp23[i] > 0) {
      ans[i]++;
      for (int j = i; j >= 0; j--) temp23[j] -= prime[primes[i]][j];
    }
  }
  for (int i = 3; i >= 0; i--)
    while (ans[i] > 0) {
      cout << primes[i];
      ans[i]--;
    }
  cout << endl;
}
