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 Scala (judge verdict: Memory Limit Exceeded)

import scala.io.StdIn

object Main {
  def func(prev: List[Int], input: (String, Char)): List[Int] =
    if(prev.length <= 1 || input._1.isEmpty) List(0)
    else {
      val next = func(prev.tail, (input._1.tail, input._2))
      if(input._1.head == input._2) (prev(1)+1) :: next
      else Math.max(next.head, prev.head) :: next
    }

  def solve(input: (String, String)): Int =
    input._2.foldLeft(List.fill(input._1.length+1)(0)){
      (prevList, ch) => func(prevList, (input._1.reverse, ch))
    }.head
  
  def main(args: Array[String]) {
    val n = StdIn.readInt()
    List.fill(n)((StdIn.readLine(), StdIn.readLine())).map(solve).foreach(println)
  }
}