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>
int n, s[20], dap[10];
char a[20];
int main() {
  int i, t, j;
  scanf("%d", &n);
  scanf("%s", a);
  s[2] = 2;
  s[3] = 3;
  s[4] = 322;
  s[5] = 5;
  s[6] = 53;
  s[7] = 7;
  s[8] = 7222;
  s[9] = 7332;
  for (i = 0; i < n; i++) {
    t = s[a[i] - '0'];
    while (t) {
      dap[t % 10]++;
      t /= 10;
    }
  }
  for (i = 9; i >= 2; i--) {
    for (j = 1; j <= dap[i]; j++) printf("%d", i);
  }
  return 0;
}
