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

def transformDigit(d):
    if d == '0' or d == '1':
        return []
    elif d == '2':
        return [2]
    elif d == '3' or d == '5' or d == '7':
        return [int(d)]
    elif d == '4':
        return [3, 2, 2]
    elif d == '6':
        return [5, 3]
    elif d == '8':
        return [7, 2, 2, 2]
    elif d == '9':
        return [7, 3, 3, 2]

if __name__ == "__main__":
    
    numLen = int(input(''))
    num = str(input(''))
    
    allDigits = []
    for d in num:
        currList = transformDigit(d)
        allDigits += currList
    
    allDigits.sort(reverse = True)
    
    for d in allDigits:
        sys.stdout.write(str(d))
    sys.stdout.write("\n")
    
    
    