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: Accepted)

import scala.io.StdIn

object Main extends App {

  private val N = 1000
  
  def lcs(x: String, y: String): Int = {
    val a = Array.fill(N+1, N+1)(0)
    val m = x.length
    val n = y.length
    var maxl = 0
    var tempX = " " + x
    var tempY = " " + y

    (1 to m).foreach{ i =>
      (1 to n).foreach{ j =>
        if(tempX(i) == tempY(j)){
          a(i)(j) = a(i-1)(j-1) + 1
        } else {
          a(i)(j) = scala.math.max(a(i-1)(j), a(i)(j-1))
        }
        maxl = scala.math.max(maxl, a(i)(j))
      }
    }
    maxl
  }

  val cnt = StdIn.readLine().toInt
  val result = (0 until cnt).map{ _ =>
    lcs(StdIn.readLine(), StdIn.readLine())
  }

  result.foreach(println)
}