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 solve(digit):
	count = [0] * 10
	for d in digit:
		for k in xrange(2, int(d) + 1):
			v = 2
			while k > 1:
				while k % v == 0:
					count[v] += 1
					k /= v
				v += 1
	out = ""
	for i in xrange(9, 1, -1):
		while count[i] > 0:
			out += str(i)
			for k in xrange(i, 1, -1):
				v = 2
				while k > 1:
					while k % v == 0:
						count[v] -= 1
						k /= v
					v += 1
	return out


n = int(raw_input())
digit = raw_input()

print(solve(digit))
