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())
mynum = input()
dic = {9: 362880, 8: 40320, 7: 5040, 6: 720, 5: 120, 4: 24, 3: 6, 2: 2,1:1,0:1}

ans = 1
udic = {7:0,5:0,3:0,2:0,"ans":1}
a = [7,5,3,2]
for i in mynum :
    ans*=dic[int(i)]
    udic["ans"] *= dic[int(i)]


for num in a :
    
    while ans%dic[num]== 0 :
        udic[num] += 1
        #print(ans)
        ans = ans//dic[num]
myans = ""

for l in a :
    myans += str(l)*udic[l]
print(myans)