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>
n = int(input())
a = input()
i = 0
e = [[0] * 11 for i in range(11) ]
for i in range(2,11):
    r = i
    while r > 1:
        k = r
        for j in range(2,11):
            while k % j == 0 and k > 0:
                e[i][j] += 1
                k = int(k / j)
        r -= 1

f = [0] * 11
for c in a:
    b = ord(c) - 48
    for i in range(2, 11):
        f[i] += e[b][i]
i = 9
while i > 1:
    while f[i] > 0:
        for j in range(2, 11):
            f[j] -= e[i][j]
        print(i, end = '')
    i -= 1
