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 defaultdict
n=int(input())
s=input()
count=defaultdict(lambda:0)
primefact=defaultdict(lambda:[])
primefact[2]=[2]
primefact[3]=[3]
primefact[4]=[2,2]
primefact[5]=[5]
primefact[6]=[2,3]
primefact[7]=[7]
primefact[8]=[2,2,2]
primefact[9]=[3,3]
for i in s:
    for j in range(2,int(i)+1):
        for k in primefact[j]:
            count[k]+=1
k=list(count.keys())
k.sort(reverse=True)
ans=""
for i in k:
    ans+=str(i)*count[i]
    for j in range(2,i):
        for k in primefact[j]:
            count[k]-=count[i]

print(ans)
