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>
n = int(raw_input())

fact = {}

fact[2] = [2]
fact[3] = [3]
fact[4] = [3, 2, 2]
fact[5] = [5]
fact[6] = [5, 3]
fact[7] = [7]
fact[8] = [7, 2, 2, 2]
fact[9] = [3, 3, 7, 2]

num = raw_input()
ans = []
for x in num:
	digit = int(x)
	if digit != 0 and digit != 1:
		transformed = fact[digit]
		ans = ans + transformed

ans.sort()
ans = ans[::-1]
print ''.join([str(x) for x in ans])

