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>
import sys

mp = {
    '0': '',
    '1': '',
    '2': '2',
    '3': '3',
    '4': '322',
    '5': '5',
    '6': '53',
    '7': '7',
    '8': '7222',
    '9': '7332'
}

sys.stdin.readline()
s = sys.stdin.readline()
for x, y in mp.items():
    s = s.replace(x, y)

sys.stdout.write(''.join(reversed(sorted(s))) + "\n")
