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data structures

hashing

strings

*3500

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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 2010-2024 Mike Mirzayanov

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