String Coloring

You are given a string S of length 2N consisting of lowercase English letters.

There are 2^{2N} ways to color each character in S red or blue. Among these ways, how many satisfy the following condition?

• The string obtained by reading the characters painted red from left to right is equal to the string obtained by reading the characters painted blue from right to left.

Constraints

• 1 \leq N \leq 18
• The length of S is 2N.
• S consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

N S

Output

Print the number of ways to paint the string that satisfy the condition.

Examples

Input

4 cabaacba

Output

4

Input

11 mippiisssisssiipsspiim

Output

504

Input

4 abcdefgh

Output

0

Input

18 aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Output

9075135300

inputFormat

Input

Input is given from Standard Input in the following format:

N S

outputFormat

Output

Print the number of ways to paint the string that satisfy the condition.

Examples

Input

4 cabaacba

Output

4

Input

11 mippiisssisssiipsspiim

Output

504

Input

4 abcdefgh

Output

0

Input

18 aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Output

9075135300

样例

4
cabaacba

4