Related Languages

You are studying two ancient languages, aiming to prove that they are closely related. You suspect that the words for "push-relabel flow algorithm" in both languages stem from a single ancestor. If so, they contain similar cores, i.e. subwords that do not differ much from each other.

Given two words $A$ and $B$, determine the maximum possible $s$, for which there are connected subwords $A'$ in $A$ and $B'$ in $B$ such that $A'$ and $B'$ have length $s$, and differ on at most $k$ positions.

The first line of input contains the number of test cases $z$ ($1 \leq z \leq 2000$). The descriptions of the test cases follow.

Every test case consists of three lines. The first line contains three numbers $n, m, k$ ($1 \le n, m \le 4000$; $0 \le k \le \min(m,n)$). In the next two lines there are two strings $A$ and $B$, of lengths $n$ and $m$, respectively, each consisting of lowercase English letters.

The total length of all the words in the input does not exceed $200\\,000$.

For each test case output a single integer -- the maximum possible length of subwords that differ on at most $k$ positions.