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

namespace aizu1
{
    public class Solution
    {
        public static void Main(string[] args)
        {
            int q = int.Parse(Console.ReadLine());
            char[] X = new char[1000];
            char[] Y = new char[1000];
            int[,] M ;

            while (q--!=0)
            {
                M = new int[1001, 1001];
                X = Console.ReadLine().ToCharArray();
                Y = Console.ReadLine().ToCharArray();

                Console.WriteLine(LCS(X, Y,M, X.Length, Y.Length));
            }
        }

        public static int LCS(char[] X, char[] Y,int[,]M, int length1, int length2)
        {
            if (length1 == 0 || length2 == 0) return 0;

            if (M[length1, length2] != 0) return M[length1, length2];
            else
            {
                int res1 = LCS(X, Y, M, length1, length2 - 1);
                int res2 = 0;
                for (int i = length1 - 1; i >= 0; i--)
                {
                    if (X[i] == Y[length2 - 1])
                    {
                        res2 = LCS(X, Y, M, i, length2 - 1) + 1;
                        break;
                    }
                }

                var res = (res1 > res2) ? res1 : res2;
                M[length1, length2] = res;
                return res;
            }
        }
    }
}