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. \InputFile The first line contains the number of test cases $z~(1 \le z \le 2000)$. 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 $2 \cdot 10^5$. \OutputFile For each test case output a single integer --- the maximum possible length of subwords that differ on at most $k$ positions.