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
input = sys.stdin.readline
read_tuple = lambda _type: map(_type, input().split(' '))
from math import factorial
    

def solve():
    changes = {
        '0': '',
        '1': '',
        '2': '2',
        '3': '3',
        '4': '322',
        '5': '5',
        '6': '53',
        '7': '7',
        '8': '7222',
        '9': '7332',
    }
    n = int(input())
    a = list(input().replace('\n', ''))
    for i in range(n):
        a[i] = changes[a[i]]
    print(''.join(sorted(''.join(a), reverse=True)))
    
if __name__ == '__main__':
    solve()