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 b[15];
void work(int a, int t2) {
  for (int i = 2; i <= a; i++) {
    int t = i;
    for (int j = 2; j <= t && t != 1; j++)
      while (t % j == 0 && t != 1) {
        b[j] += t2;
        t /= j;
      }
  }
}
int main() {
  long long a;
  cin >> a >> a;
  while (a) {
    if (a % 10 > 1) work(a % 10, 1);
    a /= 10;
  }
  for (int i = 9; i >= 2; i--)
    while (b[i]) {
      cout << i;
      work(i, -1);
    }
  cout << endl;
  return 0;
}
