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>
from math import log2

n, a, ans = int(input()), list(input()), []
for i in a:
    if int(i) > 1:
        if int(i) & 1:
            if int(i) == 9:
                ans.extend([7,3, 3, 2])
            else:
                ans.append(int(i))
        elif int(i) == 2:
            ans.append(2)
        elif int(i) in [4, 8]:
            ans.append(int(i) - 1)
            ans.extend([2 for i in range(int(log2(int(i))))])
        else:
            ans.extend([int(i) - 1, 3])

print(*sorted(ans, reverse=True), sep='')
