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>
temp=input()
inp=list(input())
dict_inp={'0':"",'1':"",'2':"2",'3':"3",'4':"322",'5':"5"
            ,'6':"53",'7':"7",'8':"7222",'9':"7332"}
for n in range(0,len(inp)):
    inp[n]=dict_inp[inp[n]]
print("".join(  (  sorted(  "".join(inp),reverse=True)  )  ) )

    
    
    