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>
input()
s, a, b, c = raw_input(), [0] * 10, '', [7, 5, 3, 2]
for j in s:
	k = int(j)
	if k in c:a[k] += 1
	elif k == 4:a[3] += 1;a[2] += 2;
	elif k == 6:a[5] += 1;a[3] += 1;
	elif k == 8:a[7] += 1;a[2] += 3;
	elif k == 9:a[7] += 1;a[3] += 2;a[2] += 1;  
for i in c:
	while a[i]:
		b += str(i)
		a[i] -= 1
print b