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,a,list1= int(input()),input(),[]
import math
for i in range(0,n):
    if int(a[i]) != 9 and int(a[i]) != 6 and int(a[i]) != 4  and int(a[i]) != 8 and int(a[i]) != 1 and int(a[i]) != 0:
        list1 = list1 + [int(a[i])]
    elif int(a[i]) == 2:
        list1 = list1 + [2]
    elif int(a[i]) == 6:
        list1 = list1 + [int(a[i])-1]+ [3]
    elif int(a[i]) == 9:
        list1 = list1 + [7] + [2] + 2*[3]
    elif int(a[i]) != 1 and int(a[i]) != 0:
        list1 = list1 + [int(a[i])-1]+ int(math.log2(int(a[i])))*[2]
        

i = [str(integer) for integer in sorted(list1, reverse=True)]
shazly = "".join(i)
print(int(shazly))