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 len, x, f[10], h[4] = {2, 3, 5, 7}, g[10];
char s[20];
int main() {
  g[0] = 1;
  for (int i = 1; i <= 9; i++) g[i] = g[i - 1] * i;
  scanf("%d\n%s", &len, s + 1);
  for (int i = 1; i <= len; i++) {
    x = s[i] - '0';
    x = g[x];
    for (; x > 1;) {
      for (int j = 3; j >= 0; j--)
        while (x % h[j] == 0) {
          f[j]++;
          x /= g[h[j]];
        }
    }
  }
  for (int i = 3; i >= 0; i--)
    for (int j = 1; j <= f[i]; j++) cout << h[i];
}
