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 sys

def fac(n):
    if(n==1):
        return 1
    else:
        return n*fac(n-1)

n = int(raw_input());
num = raw_input();
lol = 1
primes = [2, 3, 5, 7]
for i in range(0, n):
    if(num[i]=='0'):
        lol *= 1
    else:
        lol *= fac(int(num[i]))

i = 3
l = []
while(lol>1):
    k = primes[i]
    while(lol%k==0):
        l.append(k)
        lol /= fac(k)
    i = i-1
txt = ""
for item in l:
    txt += str(item)
print txt