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 math

def get_primes(prime_supr):

    is_prime = [0]*2 + [1]*prime_supr

    for i in range(2,int(math.sqrt(prime_supr)) + 1):
        if is_prime[i]:
            for j in range(i * i, prime_supr + 1, i):
                is_prime[j] = 0

    return is_prime

get_int = lambda: map(int, input().split())

n = int(input())
s = input()

d = {'0': '', '1': '', '2': '2', '3': '3', '4': '322', '5': '5', '6': '53', '7': '7', '8': '7222', '9': '7332'}

a = sorted([j for i in s for j in d[i]], reverse=True)

for i in a:
    print(i, end='')
