Vasya and Big Integers

Vasya owns three big integers — $ a, l, r $ . Let's define a partition of $ x $ such a sequence of strings $ s_1, s_2, \dots, s_k $ that $ s_1 + s_2 + \dots + 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 \le s_i \le 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 $ .

The first line contains a single integer $ a~(1 \le a \le 10^{1000000}) $ . The second line contains a single integer $ l~(0 \le l \le 10^{1000000}) $ . The third line contains a single integer $ r~(0 \le r \le 10^{1000000}) $ . It is guaranteed that $ l \le r $ . It is also guaranteed that numbers $ a, l, r $ contain no leading zeros.

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

135
1
15

2

10000
0
9

1

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 $ .