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>
L=[[],[],[2],[3],[3,2,2],[5],[3,5],[7],[2,2,2,7],[3,3,2,7]]
input()
k=[]
j=input()
for i in j:
    if i=='2':
       k+=L[2]
    elif i=='3':
       k+=L[3]
    elif i=='4':
       k+=L[4]
    elif i=='5':
       k+=L[5]
    elif i=='6':
       k+=L[6]
    elif i=='7':
       k+=L[7]
    elif i=='8':
       k+=L[8]
    elif i=='0' or i=='1':
       k+=L[0]
    else:
       k+=L[9]
k.sort()
i=len(k)-1
while i>=0:
   print(k[i],end='')
   i-=1
       