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()
p = [0, 1, 5, 7]
num2 = 0
num3 = 0
val = []
for x in a:
    t = int(x)
    if not t in p:
        while(not t in p):
            nt = t
            while t>0:
                if t%2==0:
                    t = t//2
                    num2 += 1
                else:
                    break
            while t>0:
                if t%3==0:
                    t = t//3
                    num3 += 1
                else:
                    break
            t = nt - 1
        if t!=1 and t!=0:
            val.append(t)
    else:
        if t!=0 and t!=1:
            val.append(t)
val.sort(reverse = True)
for x in val:
    print(x, end = "")
print("3"*(num3)+"2"*(num2-num3))
