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: Time Limit Exceeded)

    using System;
    using System.Collections.Generic;
    using System.Text;

    class Program
    {
        public void Proc()
        {
            int datasetCount = int.Parse(Console.ReadLine());
            string[] list1 = new string[datasetCount];
            string[] list2 = new string[datasetCount];

            for (int i = 0; i < datasetCount; i++)
            {
                list1[i] = Console.ReadLine();
                list2[i] = Console.ReadLine();
            }

            for (int i = 0; i < datasetCount; i++)
            {
                this.GetWord(list1[i], list2[i]);
            }
        }


        public void GetWord(string worda, string wordb)
        {
            this.dic = new Dictionary<string, int>();
            int ans = this.subGetWord(worda, wordb, string.Empty, 0);
            Console.WriteLine(ans);
        }

        private Dictionary<string, int> dic = new Dictionary<string, int>();
        public int subGetWord(string worda, string wordb, string tmpStr, int idx)
        {
            if (tmpStr.Length > 0)
            {
                string tmpStrSub = string.Empty;
                int subIdx = 0;
                for (int i = tmpStr.Length; i > 0; i--)
                {
                    tmpStrSub = tmpStr.Substring(0, i);
                    if (dic.ContainsKey(tmpStrSub))
                    {
                        subIdx = dic[tmpStrSub];
                        break;
                    }
                    else
                    {
                        tmpStrSub = string.Empty;
                    }
                }
                if (subIdx < 0)
                {
                    return -1;
                }
                if (tmpStr.Length > tmpStrSub.Length)
                {
                    char nxt = tmpStr[tmpStrSub.Length];
                    for (int i = subIdx; i < wordb.Length; i++)
                    {
                        if (wordb[i] == nxt)
                        {
                            tmpStrSub += nxt;
                            dic.Add(tmpStrSub, i + 1);
                            if (tmpStrSub.Length >= tmpStr.Length)
                            {
                                break;
                            }
                            nxt = tmpStr[tmpStrSub.Length];
                        }
                    }
                }
                if (tmpStrSub.Length < tmpStr.Length)
                {
                    dic[tmpStr] = -1;
                    return -1;
                }
            }
            int ans = tmpStr.Length;
            for (int i = idx; i < worda.Length; i++)
            {
                ans = Math.Max(this.subGetWord(worda, wordb, tmpStr + worda[i], i + 1), ans);
            }
            return ans;
        }

        static void Main(string[] args)
        {
            Program prg = new Program();
            prg.Proc();
        }
    }