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():
	raw_input()
	l = [0 for _ in range(10)]
	for c in raw_input():
		x = int(c)
		if x == 9:
			l[7]+=1
			l[3]+=2
			l[2]+=1
		elif x == 8:
			l[7]+=1
			l[2]+=3
		elif x == 6:
			l[5]+=1
			l[3]+=1
		elif x == 4:
			l[3]+=1
			l[2]+=2
		elif x > 1:
			l[x]+=1
	r = ''
	for d, m in enumerate(l):
		r = m*str(d) + r
	print r


if __name__ == '__main__':
	main()