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H. Palindromic Magic
time limit per test
2.5 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

After 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.