little-bear-and-strings
Source: hackerearth
Difficulty: HARD

Little bear has got a big string S as his birthday present. Also, he personally loves all those strings that start with T1 and end with T2, and calls them good. Now, he would like most the birthday present has maximum number of good substrings. Also, he is not the kind of "bear"(:P) that would easily get fooled by substrings with different start and end positions. He would only count a string once, irrespective of its number of occurences. More formally, he wants to determine the number of distinct  good substrings.

Input: 
The input file contains multiple test cases that end with EOF.
Each test case comprises of 3 lines each containing S, T1 and T2 respectively.

Output: 
Output the required answer in a new line for every test case.

Constraints: 
1 ≤ |S| , |T1|, |T2| ≤ 300000 
The maximum input file size is < 2 MB.

Note: 
 1. The input string contains only letters a-z. 
 2. A substring is any non-empty contiguous subsequence of given string. Read more here.  
 3. Two substrings s1 and s2 are different from one another if either their lengths are unequal or there is at least one index i such that s1[i] is not equal to s2[i]. This is irrespective of start and end points of substring.

SAMPLE INPUT
hammer
ham
mer
gogoa
go
z
gogoa
g
o

SAMPLE OUTPUT
1
0
2

Explanation

Distinct substrings being referred are : 
case 1: "hammer"
case 2: None
case 3: "go", "gogo"