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.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;

namespace AOJ
{
    class Program
    {
        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }

        static long[] f;
        static void Main(string[] args)
        {
            var Q = Sarray()[0];
            for (var i = 0; i < Q; ++i)
            {
                var len1 = ReadLine();
                var len2 = ReadLine();
                var w = len1.Length;
                var h = len2.Length;
                var mtch = new int[w, h];
                for (var j = 0; j < w; ++j)
                {
                    for (var k = 0; k < h; ++k)
                    {
                        if (len1[j] == len2[k])
                        { mtch[j, k] = 1; }
                    }
                }
                var rui = new int[w + 1, h + 1];
                for(var j=1;j<w+1;++j)
                {
                    for (var k = 1; k < h + 1; ++k)
                    {
                        rui[j, k] = Math.Max(Math.Max(rui[j - 1, k], rui[j, k - 1]), rui[j - 1, k - 1] + mtch[j - 1, k - 1]);
                    }
                }
#if DEBUG
                for (var j = 0; j < w; ++j)
                {
                    for (var k = 0; k < h; ++k)
                    {
                        Write(mtch[j, k]+", ");
                    }
                    WriteLine();
                }
                for (var j = 0; j < w+1; ++j)
                {
                    for (var k = 0; k < h+1; ++k)
                    {
                        Write(rui[j, k] + ", ");
                    }
                    WriteLine();
                }
#endif
                WriteLine(rui[w, h]);
            }
        }
    }
}