String Coloring

AtCoder

IDagc026_c

Time3000ms

Memory256MB

Difficulty—

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: $N$ $S$ [samples]

Samples

Input #1

4
cabaacba

Output #1

4

There are four ways to paint the string, as follows:

*   cabaacba
*   cabaacba
*   cabaacba
*   cabaacba

Input #2

11
mippiisssisssiipsspiim

Output #2

Input #3

4
abcdefgh

Output #3

Input #4

18
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Output #4

9075135300

The answer may not be representable as a $32$\-bit integer.

API Response (JSON)

{
  "problem": {
    "name": "String Coloring",
    "description": {
      "content": "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 ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc026_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a string $S$ of length $2N$ consisting of lowercase English letters.\nThere are $2^{2N}$ ways to color each character in $S$ red or blue. Among these ways, how many satisfy the following ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments