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 C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

namespace CSharpSample01
{


    class Program
    {

        
        static int Solve(string X, string Y)
        {
            int xn = X.Length;
            int yn = Y.Length;

            int[,] dp = new int[xn + 1, yn + 1];

            dp[0, 0] = 0;
            
            for(int i = 1; i <= xn; i++)
            {
                for(int j = 1; j <= yn; j++)
                {
                    if(X[i - 1] == Y[j - 1])
                    {
                        dp[i, j] = dp[i - 1, j - 1] + 1;
                    }
                    else
                    {
                        dp[i, j] = Math.Max(dp[i - 1, j], dp[i, j - 1]);
                    }
                }
            }

            return dp[xn, yn];
        }



        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());

            for(int i = 0; i < n; i++)
            {
                string X = Console.ReadLine();
                string Y = Console.ReadLine();

                Console.WriteLine(Solve(X, Y));
            }
                      
        }
    }
}