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>
bbbbbbbbbbbbbbbbbb = input()
n  = input()
dic = {"4":"322","6":"35","8":"2227","9":"3327"}
res = ""
for i in n:
	if int(i)!=0 and int(i)!=1 and int(i)!=9 and (int(i)%2==1 or int(i)==2):
		res+=i
	elif int(i)!=0 and int(i)!=1 and i in dic:
		res+=dic[i]
ls = [x for x in res]
t = ""
ls.sort()
for x in range(len(res)-1,-1,-1):
	t+=ls[x]
print(t)	