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 tl(sn):
	if sn=='0' or sn=='1':
		return ''
	elif sn=='4':
		return '322'
	elif sn=='6':
		return '53'
	elif sn=='8':
		return '7222'
	elif sn=='9':
		return '7332'
	else:
		return sn
		
def ts(s):
	ns=[]
	for c in s:
		ns+=[x for x in tl(c)]
	ns.sort(reverse=1)
	return ''.join(ns)

input()
print(ts(input()))