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 descompunere(nr):
    ls = []
    while nr % 2 == 0:
        ls.append(2)
        nr //= 2
    for i in range(3, nr + 1, 2):
        while nr % i == 0:
            nr //= i
            ls.append(i)
    return ls


def factorial(nr):
    l = []
    for i in range(2, nr + 1):
        l.extend(descompunere(i))
    return l


def refactorizare(l):
    def remake(nr):
        s = descompunere(nr)
        for i in s:
            l.pop(l.index(i))

    v = []
    while len(l) > 0:
        v.append(l[0])
        for i in range(l[0], 1, -1):
            try:
                l.pop(l.index(i))
            except ValueError:
                remake(i)
    return v


s = input()
s = input()

v = []
for i in s:
    v.extend(factorial(int(i)))
v.sort(reverse=True)
s = refactorizare(v)
for i in s:
    print(i, end="")
