You are given a string of length n and a dictionary containing k words. In how many ways can you create the string using the words?

Input

The first input line has a string containing n characters between a–z.

The second line has an integer k: the number of words in the dictionary.

Finally there are k lines describing the words. Each word is unique and consists of characters a–z.

Output

Print the number of ways modulo 10^9+7.

Constraints

• 1 \le n \le 5000
• 1 \le k \le 10^5
• the total length of the words is at most 10^6

Example

Input:

ababc
4
ab
abab
c
cb

Output:

2

Explanation: The possible ways are ab+ab+c and abab+c.