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>
def main():
	
	d = {'2':['2'],
		 '3':['3'],
		 '4': ['3','2','2'],
		 '5' :['5'],
		 '6' : ['5','3'],
		 '7' : ['7'],
		 '8' :['7','2','2','2'],
		 '9' :['7','3','3','2']
		 }
	n = int(input())
	a = list(input())
	res = []
	for x in a:
		if x not in ['0', '1']:				
			res = res + d[x]
	res = sorted(res)[::-1]
	print(''.join(res))




if __name__ == '__main__':
	main()