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>
a = input("")
b = input("")
outstring = ""
for value in b:
    if value == "1":
        continue
    elif value == "2":
        outstring = outstring + "2"
    elif value == "3":
        outstring = outstring + "3"
    elif value == "4":
        outstring = outstring + "3" + "2" + "2"
    elif value == "5":
        outstring = outstring + "5"
    elif value == "6":
        outstring = outstring + "5" + "3"
    elif value == "7":
        outstring = outstring + "7"
    elif value == "8":
        outstring = outstring + "7" + "2" + "2" + "2"
    elif value == "9":
        outstring = outstring + "7" + "3" + "3" + "2"
t = [i for i in outstring]
t.sort()
t.reverse()
print(''.join(t))
