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=int(input())
a=str(input())
d=[];answer=""

for i in range(n):
    k=int(a[i])
    if k==1:
        continue
    else:
        for l in range(2,k+1):
            k=l
            while k!=1:
                for j in range(2,10):
                    if k%j==0:
                        k//=j
                        d.append(j)
                        break            
d.sort(reverse=True)
#print(d)

while len(d)!=0:
    answer+=str(d[0])
    
    for i in range(d[0],1,-1):
        k=i
        while k!=1:
            for j in range(2,10):
                if k%j==0:
                    del(d[d.index(j)])
                    k//=j
print(answer)
    
    
            