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>
n=int(raw_input())
A=dict()
A['2']=[2]
A['3']=[3]
A['4']=[3,2,2]
A['5']=[5]
A['6']=[5,3]
A['7']=[7]
A['8']=[7,2,2,2]
A['9']=[7,3,3,2]
a=raw_input()
x=[]
for i in a:
    if i!='0' and i!='1':
        x.extend(A[i])
x=sorted(x,reverse=True)
x=[str(i) for i in x]
y=''
for i in x:
    y+=i
print y
