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>
from collections import Counter
x=int(input())
n=input()
s=""
for i in n:
    if i=="2":
        s+="2"
    elif i=="3":
        s+="3"
    elif i=="4":
        s+="322"
    elif i=="5":
        s+="5"
    elif i=="6":
        s+="53"
    elif i=="7":
        s+="7"
    elif i=="8":
        s+="7222"
    elif i=="9":
        s+="7332"
s=list(s)
s.sort()
s=s[::-1]
print("".join(s))
        