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(int(str(input())))
arr=[]
f=[[],[],[2],[2,3],[2,2,2,3],[2,2,2,3,5],
   [2,2,2,2,3,3,5],[2,2,2,2,3,3,5,7],
   [2,2,2,2,2,2,2,3,3,5,7],[2,2,2,2,2,2,2,3,3,3,3,5,7]]
for i in a:
    k=f[int(i)]
    for j in range(len(k)):
        arr.append(k[j])
arr.sort(reverse=True)
answer=''
while len(arr)!=0:
    k=arr[0]
    answer+=str(k)
    h=f[k]
    for j in range(len(h)):
        del(arr[arr.index(h[j])])
print(answer)