Problem link, link: https://codeforces.net/contest/1679/problem/E

Part 1: Notations

$$$s$$$: The original string that might contain '?'.

$$$s[i,j] (i \leq j)$$$: The substring including $$$s[i]$$$ and $$$s[j]$$$: $$$(s[i], s[i+1],..., s[j])$$$.

$$$t$$$: The query string.

We also define some notations that will be clarified in the Part 2:

$$$ok[i,j]$$$: A $$$2D$$$ bool array indicating whether $$$s[i,j]$$$ is valid or not. We will define the word "valid" in Part 2. If $$$s[i,j]$$$ is valid, then $$$ok[i,j]$$$ is true, if $$$s[i,j]$$$ is invalid, then $$$ok[i,j]$$$ is false.

$$$set[i, j]$$$: The required character set to make $$$s[i,j]$$$ a palindrome.

$$$free[i, j]$$$: The number of free places. We will define the terminology "free places" in part 2.

Part 2: ok, set and free

We call a substring $$$s[i,j]$$$ valid if and only if:

For every $$$x$$$ such that $$$i \leq x \leq j$$$, if $$$s[x] \neq '?' && s[i+j-x] \neq '?'$$$, then $$$s[x] = s[i+j-x]$$$.