Patterns

A pattern of size $n$ is a string of length $n$, where each character belongs to the set \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f, g, ?\}. Patterns are converted into strings of digits according to the following rules:

• Characters $0$ to $9$ can be converted only to themselves.

• Symbol $a$ can be converted to any of the symbols $0$, $1$, $2$, $3$.

• Symbol $b$ can be converted to any of the symbols $1$, $2$, $3$, $4$.

• Symbol $c$ can be converted to any of the symbols $2$, $3$, $4$, $5$.

• Symbol $d$ can be converted to any of the symbols $3$, $4$, $5$, $6$.

• Symbol $e$ can be converted to any of the symbols $4$, $5$, $6$, $7$.

• Symbol $f$ can be converted to any of the symbols $5$, $6$, $7$, $8$.

• Symbol $g$ can be converted to any of the symbols $6$, $7$, $8$, $9$.

• Symbol $?$ can be converted to any of the symbols from $0$ to $9$.

Given two patterns: p_1 and p_2. Let S_1 be the set of strings that can be obtained from p_1 according to the rules described, and S_2 the set of strings obtained from p_2. Find the number of strings contained in both sets.