Score : 150150150 points

Problem Statement

The definition of an 11/22 string in this problem is the same as in Problems C and E.

A string TTT is called an 11/22 string when it satisfies all of the following conditions:

• ∣T∣|T|∣T∣ is odd. Here, ∣T∣|T|∣T∣ denotes the length of TTT.
• The 111-st through (∣T∣+12−1)(\frac{|T|+1}{2} - 1)(2∣T∣+1​−1)-th characters are all 1.
• The (∣T∣+12)(\frac{|T|+1}{2})(2∣T∣+1​)-th character is /.
• The (∣T∣+12+1)(\frac{|T|+1}{2} + 1)(2∣T∣+1​+1)-th through ∣T∣|T|∣T∣-th characters are all 2.

For example, 11/22, 111/222, and / are 11/22 strings, but 1122, 1/22, 11/2222, 22/11, and //2/2/211 are not.

Given a string SSS of length NNN consisting of 1, 2, and /, determine whether SSS is an 11/22 string.

Constraints

• 1≤N≤1001 \leq N \leq 1001≤N≤100
• SSS is a string of length NNN consisting of 1, 2, and /.

Input

The input is given from Standard Input in the following format:

NNN
SSS

Output

If SSS is an 11/22 string, print Yes; otherwise, print No.

Sample Input 1Copy

Copy

5
11/22

Sample Output 1Copy

Copy

Yes

11/22 satisfies the conditions for an 11/22 string in the problem statement.

Sample Input 2Copy

Copy

1
/

Sample Output 2Copy

Copy

Yes

/ satisfies the conditions for an 11/22 string.

Sample Input 3Copy

Copy

4
1/22

Sample Output 3Copy

Copy

No

1/22 does not satisfy the conditions for an 11/22 string.

Sample Input 4Copy

Copy

5
22/11

Sample Output 4Copy

Copy

No