Rating changes for the last round are temporarily rolled back. They will be returned soon.
×

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
H. Palindromic Magic

time limit per test

2.5 secondsmemory limit per test

1024 megabytesinput

standard inputoutput

standard outputAfter learning some fancy algorithms about palindromes, Chouti found palindromes very interesting, so he wants to challenge you with this problem.

Chouti has got two strings $$$A$$$ and $$$B$$$. Since he likes palindromes, he would like to pick $$$a$$$ as some non-empty palindromic substring of $$$A$$$ and $$$b$$$ as some non-empty palindromic substring of $$$B$$$. Concatenating them, he will get string $$$ab$$$.

Chouti thinks strings he could get this way are interesting, so he wants to know how many different strings he can get.

Input

The first line contains a single string $$$A$$$ ($$$1 \le |A| \le 2 \cdot 10^5$$$).

The second line contains a single string $$$B$$$ ($$$1 \le |B| \le 2 \cdot 10^5$$$).

Strings $$$A$$$ and $$$B$$$ contain only lowercase English letters.

Output

The first and only line should contain a single integer — the number of possible strings.

Examples

Input

aa

aba

Output

6

Input

aaba

abaa

Output

15

Note

In the first example, attainable strings are

- "a" + "a" = "aa",
- "aa" + "a" = "aaa",
- "aa" + "aba" = "aaaba",
- "aa" + "b" = "aab",
- "a" + "aba" = "aaba",
- "a" + "b" = "ab".

In the second example, attainable strings are "aa", "aaa", "aaaa", "aaaba", "aab", "aaba", "ab", "abaa", "abaaa", "abaaba", "abab", "ba", "baa", "baba", "bb".

Notice that though "a"+"aa"="aa"+"a"="aaa", "aaa" will only be counted once.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jul/30/2021 16:27:16 (h2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|