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>
import os, math

def is_prime(a):
    return all(a % i for i in xrange(2, a))
def primes(n):
    primfac = []
    d = 2
    while d*d <= n:
        while (n % d) == 0:
            primfac.append(d)  # supposing you want multiple factors repeated
            n //= d
        d += 1
    if n > 1:
       primfac.append(n)
    return primfac

n = input()
a = raw_input()
prime_list = []
for i in xrange(0, n):
    prime_list += primes(math.factorial(int(a[i])))
                         
prime_list.sort(reverse=True)
#print prime_list

x = 0
while len(prime_list) > 0:
    n = prime_list[0]
    temp = n
    #print prime_list
    while temp > 1:
        if is_prime(temp) == True:
            prime_list.remove(temp)
        else:
            prime_fac = primes(temp)
            for e in prime_fac:
                prime_list.remove(e)
        temp -= 1
    x = x * 10 + n
print x
            
