A12834. You Are Given Some Strings...

You are given a string $t$ and $n$ strings $s_1, s_2, \dots, s_n$ . All strings consist of lowercase Latin letters.

Let $f(t, s)$ be the number of occurences of string $s$ in string $t$ . For example, $f('\text{aaabacaa}', '\text{aa}') = 3$ , and $f('\text{ababa}', '\text{aba}') = 2$ .

Calculate the value of $\sum\limits_{i=1}^{n} \sum\limits_{j=1}^{n} f(t, s_i + s_j)$ , where $s + t$ is the concatenation of strings $s$ and $t$ . Note that if there are two pairs $i_1$ , $j_1$ and $i_2$ , $j_2$ such that $s_{i_1} + s_{j_1} = s_{i_2} + s_{j_2}$ , you should include both $f(t, s_{i_1} + s_{j_1})$ and $f(t, s_{i_2} + s_{j_2})$ in answer.

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

The second line contains integer $n$ ( $1 \le n \le 2 \cdot 10^5$ ).

Each of next $n$ lines contains string $s_i$ ( $1 \le |s_i| \le 2 \cdot 10^5$ ).

It is guaranteed that $\sum\limits_{i=1}^{n} |s_i| \le 2 \cdot 10^5$ . All strings consist of lowercase English letters.

Print one integer — the value of $\sum\limits_{i=1}^{n} \sum\limits_{j=1}^{n} f(t, s_i + s_j)$ .