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>
from math import factorial
n = input()
fact = [factorial(i) for i in range(2,10)]
dd = [[0,0,0,0],[0,0,0,0],[1,0,0,0],[1,1,0,0],[3,1,0,0],[3,1,1,0],[4,2,1,0],[4,2,1,1],[7,2,1,1],[7,4,1,1]]
dig = [2,3,5,7]		
d = [0,0,0,0]
n = raw_input()
for s in n: d = [x+y for x,y in zip(d,dd[int(s)])]

ans = ''
for i in range(3,-1,-1):
	while d[i]>0:
		d = [x-y for x,y in zip(d,dd[dig[i]])]
		ans = ans+str(dig[i])
		
print ans		