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>
t=1
for _ in range(t):
    l=int(input())
    a=[i for i in input()]
    ans=[]
    for i in a:
        if(i=='2'):
            ans=ans+['2']
        elif(i=='3'):
            ans=ans+['3']
        elif(i=='4'):
            ans=ans+['3','2','2']
        elif(i=='5'):
            ans=ans+['5']
        elif(i=='6'):
            ans=ans+['5','3']
        elif(i=='7'):
            ans=ans+['7']
        elif(i=='8'):
            ans=ans+['7','2','2','2']
        elif(i=='9'):
            ans=ans+['7','3','3','2']
        ans.sort(reverse=True)
    print(''.join(ans))
        
    