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 = input()
s = raw_input()
dic = {
  "0" : "",
  "1" : "",
  "2" : "2",
  "3" : "3",
  "4" : "223",
  "5" : "5",
  "6" : "35",
  "7" : "7",
  "8" : "2227",
  "9" : "2337"
}

ans = ""
for i in xrange(n):
  ans += dic[s[i]]
ans = list(ans)
ans.sort(reverse=True)
print "".join(ans)


