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>
prime = [2, 3, 5, 7]
cnt   = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

def phan_tich_thua_so_nto (n, kind) : 
    for j in prime : 
        while n % j == 0 :
            n /= j
            cnt[j] += kind

def solve(n, a) :
    a = list(a)
    a = list(map(int, a))

    for i in a : 
        for j in range (1, i + 1, 1) : phan_tich_thua_so_nto(j, 1)

    res = ''
    for i in range (3, 0 - 1, -1) :
        while(cnt[prime[i]] > 0) :
            for j in range (prime[i], 1 - 1, -1) : phan_tich_thua_so_nto(j, -1)
            res += str(prime[i])
    return res

def drazil_and_factorial(n, a) : 
    return solve(n, a)

if __name__ == '__main__' :
    n = int(input())
    a = input()
    print(drazil_and_factorial(n, a))