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>
pockets = [0]*10
convert = [[],[],[2],[3],[2,2],[5],[2,3],[7],[2,2,2],[3,3]]
primes = [2,3,5,7] #check for these
input() #ignore
strang = input()
for c in strang:
    integ = ord(c)-0x30
    for d in range(integ+1):
        for e in convert[d]:
            pockets[e] += 1
newstr = ""
for p in range(len(primes)-1, -1, -1):
    prime = primes[p]
    if pockets[prime]:
        while pockets[prime]:
            for q in range(2,prime+1):
                for r in convert[q]:
                    pockets[r]-=1
            newstr += str(prime)
print(newstr)