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())
num=input()
cnt=[0]*10
def inc(a):
         if(a<2):
                  return
         global cnt
         if a==2:
               cnt[2]+=1
         elif a==3:
                  cnt[3]+=1
         elif a==4:
                  cnt[2]+=2
         elif a==5:
                  cnt[5]+=1
         elif a==6:
                  cnt[2]+=1
                  cnt[3]+=1
         elif a==8:
                  cnt[2]+=3
         elif a==9:
                  cnt[3]+=2
         else:
                  cnt[7]+=1
         inc(a-1)
def dec(a):
         if(a<2):
                  return
         global cnt
         if a==2:
               cnt[2]-=1
         elif a==3:
                  cnt[3]-=1
         elif a==4:
                  cnt[2]-=2
         elif a==5:
                  cnt[5]-=1
         elif a==6:
                  cnt[2]-=1
                  cnt[3]-=1
         elif a==8:
                  cnt[2]-=3
         elif a==9:
                  cnt[3]-=2
         else:
                  cnt[7]-=1
         dec(a-1)
for i in num:
         inc(int(i))
for i in range(9,-1,-1):
         while(cnt[i]>0):
                  print(i,end="")
                  dec(i)