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.

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.

Palindromic Magic

Examples