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E. You Are Given Some Strings...
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Input

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.

Output

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

Examples
Input
aaabacaa
2
a
aa
Output
5
Input
aaabacaa
4
a
a
a
b
Output
33