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>
from functools import reduce
from math import factorial

def factor(n):
    factors = [0] * 8
    for i in range(2, 8):
        while n % i == 0:
            factors[i] += 1
            n //= i
    return factors

input()
f = factor(reduce(lambda a, b: a * factorial(int(b)), input().strip(), 1))
digits = []
for i in range(7, 1, -1):
    t = factor(factorial(i))
    digits += [i] * f[i]
    f = [f[j] - f[i] * t[j] for j in range(8)]
print(*sorted(digits, reverse = True), sep = '')
