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 sqrt; from itertools import count, islice

def isPrime(n):
    return n > 1 and all(n%i for i in islice(count(2), int(sqrt(n)-1)))
def bib():
     while '8' in s:
          s.append('2')
          s.append('2')
          s.append('2')
          s.append('7')
          s.remove('8')
     while '4' in s:
          s.append('2')
          s.append('2')
          s.append('3')
          s.remove('4')
     while '6' in s:
          s.append('3')
          s.append('5')
          s.remove('6')
     while '9' in s:
          s.append('2')
          s.append('3')
          s.append('3')
          s.append('7')
          s.remove('9')
n = int(input())
s = list(input())
if '1' in s:
     s.remove('1')
if '0' in s:
     s.remove('0')
bib()
while '0' in s:
     s.remove('0')
while '1' in s:
     s.remove('1')
print("".join(sorted(s , reverse = True)))
