Separate String

Time Limit : 2 sec, Memory Limit : 524288 KB

Separate String

You are given a string $t$ and a set $S$ of $N$ different strings. You need to separate $t$ such that each part is included in $S$.

For example, the following 4 separation methods satisfy the condition when $t = abab$ and $S = \{a, ab, b\}$.

  • $a,b,a,b$
  • $a,b,ab$
  • $ab,a,b$
  • $ab,ab$

Your task is to count the number of ways to separate $t$. Because the result can be large, you should output the remainder divided by $1,000,000,007$.

Input

The input consists of a single test case formatted as follows.

$N$
$s_1$
:
$s_N$
$t$

The first line consists of an integer $N$ ($1 \leq N \leq 100,000$) which is the number of the elements of $S$. The following $N$ lines consist of $N$ distinct strings separated by line breaks. The $i$-th string $s_i$ represents the $i$-th element of $S$. $s_i$ consists of lowercase letters and the length is between $1$ and $100,000$, inclusive. The summation of length of $s_i$ ($1 \leq i \leq N$) is at most $200,000$. The next line consists of a string $t$ which consists of lowercase letters and represents the string to be separated and the length is between $1$ and $100,000$, inclusive.

Output

Calculate the number of ways to separate $t$ and print the remainder divided by $1,000,000,007$.

Sample Input 1

3
a
b
ab
abab

Output for Sample Input 1

4

Sample Input 2

3
a
b
c
xyz

Output for Sample Input 2

0

Sample Input 3

7
abc
ab
bc
a
b
c
aa
aaabcbccababbc

Output for Sample Input 3

160

Sample Input 4

10
a
aa
aaa
aaaa
aaaaa
aaaaaa
aaaaaaa
aaaaaaaa
aaaaaaaaa
aaaaaaaaaa
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Output for Sample Input 4

461695029

Source: JAG Practice Contest for ACM-ICPC Asia Regional 2017 , Japan, 2017-11-19
http://acm-icpc.aitea.net/
https://jag2017autumn.contest.atcoder.jp/