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>
input()
num = input()
factorials = (
	('2'),
	('3'),
	('3', '2', '2'),
	('5'),
	('5', '3'),
	('7'),
	('7', '2', '2', '2'),
	('7', '3', '3', '2')
)
numbers = []
for i in num:
	if i > '1':
		for j in factorials[int(i) - 2]:
			numbers.append(j)
numbers.sort(reverse=True)
for i in numbers:
	print(i, end="", sep="")
#n, m = map(int, input().split())