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 mapping(a):
    if a == "0": return ""
    if a == "1": return ""
    if a == "2" or a == "3" or a == "5" or a == "7": return a
    if a == "4": return "322"
    if a == "6": return "53"
    if a == "8": return "7222"
    if a == "9": return "7332"

n, a, b = input(), raw_input(), ""
for x in a: b += mapping(x)
print "".join(sorted(b, reverse = True))
