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())
s=input()
L=[]
L.append([])
L.append([])
L.append([2])
L.append([3])
L.append([2,2])
L.append([5])
L.append([2,3])
L.append([7])
L.append([2,2,2])
L.append([3,3])
A=[]
for i in range(n):
    x = int(s[i])
    for j in range(2,x+1):
        for item in L[j]:
            A.append(item)
A.sort(reverse=True)
ans=""
while(len(A)>0):
    x = A[0]
    ans+=str(x)
    x-=1
    Ind = [0]
    while(x>1):
        for item in L[x]:
            for i in range(1,len(A)):
                if(A[i]==item and i not in Ind):
                    Ind.append(i)
                    break
        x-=1
    Ind.sort()

    for i in range(len(Ind)-1,-1,-1):
        A.pop(Ind[i])
print(ans)
        
