← Home
write a go solution for Description:
Vasya owns three big integers — a,l,r. Let's define a partition of x such a sequence of strings s_1,s_2,...,s_k that s_1+s_2+...+s_k=x, where + is a concatanation of strings. s_i is the i-th element of the partition. For example, number 12345 has the following partitions: ["1", "2", "3", "4", "5"], ["123", "4", "5"], ["1", "2345"], ["12345"] and lots of others.

Let's call some partition of a beautiful if each of its elements contains no leading zeros.

Vasya want to know the number of beautiful partitions of number a, which has each of s_i satisfy the condition l<=s_i<=r. Note that the comparison is the integer comparison, not the string one.

Help Vasya to count the amount of partitions of number a such that they match all the given requirements. The result can be rather big, so print it modulo 998244353.

Input Format:
The first line contains a single integer a~(1<=a<=10^1000000).

The second line contains a single integer l~(0<=l<=10^1000000).

The third line contains a single integer r~(0<=r<=10^1000000).

It is guaranteed that l<=r.

It is also guaranteed that numbers a,l,r contain no leading zeros.

Output Format:
Print a single integer — the amount of partitions of number a such that they match all the given requirements modulo 998244353.

Note:
In the first test case, there are two good partitions 13+5 and 1+3+5.

In the second test case, there is one good partition 1+0+0+0+0.. Output only the code with no comments, explanation, or additional text.