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>
def fatorial(n):
    if n == 1 or n == 0:
        return [1]
    else:
        return [n] + fatorial(n-1)


def expande(n, div=2):
    if n == 1:
        return [1]
    else:
        if n % div == 0:
            return [div] + expande(n//div)
        else:
            return expande(n, div+1)

num = int(input())
n = input()

lista_fatorada = []

for x in n:
    for l in fatorial(int(x)):
        lista_fatorada += expande(l)
lista_fatorada.sort(reverse=True)
lista_fatorada += [1]*len(lista_fatorada)
lista_copia = lista_fatorada.copy()
ans = []


while lista_fatorada.count(1) != len(lista_fatorada):
    x = lista_fatorada[0]
    if x == 1:
        break
    ans.append(x)
    lista_expandida = []
    for i in fatorial(x):
        lista_expandida += expande(i)
    for i in lista_expandida:
        lista_copia.remove(i)
    lista_fatorada = lista_copia.copy()

print(''.join(list(map(str, ans))))








