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 factorial(n):
	n = list(str(n))
	n = map(int,n)
	a = []
	for i in n:
		if(i != 0 and i != 1):
			if(i == 4):
				a.append("322")
			elif(i == 6):
				a.append("53")
			elif(i == 8):
				a.append("7222")
			elif(i == 9):
				a.append("7332")
			else:
				a.append(str(i))
	b = (''.join(a))
	b = list(b)
	for i in b:
		i = int(i)
	b = sorted(b)
	b = b[::-1]
	print(''.join(b))

n = int(input())
x = int(input())

factorial(x)