Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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;
using System.Text;

namespace Aizu
{
    class Program
    {
        static void Main(string[] args)
        {
            var q = int.Parse(Console.ReadLine());
            var answers = new List<int>();

            for(var i = 0; i < q; i++)
            {
                var x = Console.ReadLine();
                var y = Console.ReadLine();

                var lcsLength = new int[x.Length + 1, y.Length + 1];

                for(var j = 1; j <= x.Length; j++)
                {
                    for(var k = 1; k <= y.Length; k++)
                    {
                        if(x[j - 1] == y[k - 1])
                        {
                            lcsLength[j, k] = lcsLength[j - 1, k - 1] + 1;
                        }

                        lcsLength[j, k] = Math.Max(lcsLength[j, k], Math.Max(lcsLength[j - 1, k], lcsLength[j, k - 1]));
                    }
                }

                answers.Add(lcsLength[x.Length, y.Length]);
            }

            answers.ForEach(value => Console.WriteLine(value));
        }
    }
}