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>
import copy
n = int(input())
a = int(input())
c = copy.copy(a)
l = []
i = 0
while c!=0:
    l.append(c%10)
    c//=10
while 1 in l:
    l.remove(1)
while 0 in l:
    l.remove(0)
while 9 in l :
    l.remove(9)
    l.append(7)
    l.append(3)
    l.append(3)
    l.append(2)
while 8 in l:
    l.remove(8)
    l.append(7)
    l.append(2)
    l.append(2)
    l.append(2)
while 6 in l:
    l.remove(6)
    l.append(5)
    l.append(3)
while 4 in l:
    l.remove(4)
    l.append(3)
    l.append(2)
    l.append(2)
l.sort(reverse = True)
k = 0
for i in range(len(l)):
    k +=(10**i)*l[len(l)-1-i]
print(k)
    
    