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>
digit=int(input())
number=int(input())
newNumber=0
while number>0:
    x=number%10
    number=number//10
    if x!=0 and x!=1:
        if x==2 or x==3 or x==5 or x==7:
            newNumber=newNumber*10+x
        elif x==4:
            newNumber=newNumber*1000+223
        elif x==6:
            newNumber=newNumber*100+53
        elif x==8:
            newNumber=newNumber*10000+2227
        elif x==9:
            newNumber=newNumber*10000+3327
a=list(str(newNumber))
a.sort()
a.reverse()
l=len(a)
N=0
for i in range(0,l):
    N=N*10+int(a[i])
print(N)