Problem:
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Longest Common Subsequence

For given two sequences $X$ and $Y$, a sequence $Z$ is a common subsequence of $X$ and $Y$ if $Z$ is a subsequence of both $X$ and $Y$. For example, if $X = \{a,b,c,b,d,a,b\}$ and $Y = \{b,d,c,a,b,a\}$, the sequence $\{b,c,a\}$ is a common subsequence of both $X$ and $Y$. On the other hand, the sequence $\{b,c,a\}$ is not a longest common subsequence (LCS) of $X$ and $Y$, since it has length 3 and the sequence $\{b,c,b,a\}$, which is also common to both $X$ and $Y$, has length 4. The sequence $\{b,c,b,a\}$ is an LCS of $X$ and $Y$, since there is no common subsequence of length 5 or greater.

Write a program which finds the length of LCS of given two sequences $X$ and $Y$. The sequence consists of alphabetical characters.

Input

The input consists of multiple datasets. In the first line, an integer $q$ which is the number of datasets is given. In the following $2 \times q$ lines, each dataset which consists of the two sequences $X$ and $Y$ are given.

Output

For each dataset, print the length of LCS of $X$ and $Y$ in a line.

Constraints

$1 \leq q \leq 150$

$1 \leq$ length of $X$ and $Y$ $\leq 1,000$

$q \leq 20$ if the dataset includes a sequence whose length is more than 100

Sample Input 1

3
abcbdab
bdcaba
abc
abc
abc
bc

Sample Output 1

4
3
2

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in OCaml (judge verdict: Accepted)

let lcs s1 s2 =
  let l1 = String.length s1 in
  let l2 = String.length s2 in
  let dp = Array.make_matrix (l1+1) (l2+1) 0 in
  let rec iter i j =
    if i = l1 + 1 then dp.(l1).(l2)
    else if j = l2 + 1 then iter (i+1) 1
    else begin
        if s1.[i-1] = s2.[j-1] then
          dp.(i).(j) <- dp.(i-1).(j-1) + 1
        else
          dp.(i).(j) <- max dp.(i-1).(j) dp.(i).(j-1);
        iter i (j+1)
      end
  in iter 1 1
                
let () =
  let n = read_int () in
  let rec iter i =
    if i = 0 then ()
    else
      let s1 = read_line () in
      let s2 = read_line () in
      lcs s1 s2 |> string_of_int |> print_endline;
      iter (i-1)
  in iter n