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.IO;

namespace Dynamic_Programming
{
    class Longest_Common_Subsequence
    {
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            for (int i = 0; i < n; i++)
            {
                var X = Console.ReadLine();
                var Y = Console.ReadLine();

                Console.WriteLine(LongestCommonSubseq(X, Y));
            }
            Console.Out.Flush();
        }

        static int LongestCommonSubseq(string x, string y)
        {
            var row = x.Length;
            var col = y.Length;

            var l = new int[row, col];
            if (x[0] == y[0]) l[0, 0] = 1;
            for (int i = 1; i < row; i++)
                if (x[i] == y[0] || l[i - 1, 0] == 1) l[i, 0] = 1;
            for (int i = 1; i < col; i++)
                if (x[0] == y[i] || l[0, i - 1] == 1) l[0, i] = 1;

            for (int i = 1; i < row; i++)
                for (int j = 1; j < col; j++)
                    if (x[i] == y[j]) l[i, j] = l[i - 1, j - 1] + 1;
                    else l[i, j] = (l[i - 1, j] > l[i, j - 1]) ? l[i - 1, j] : l[i, j - 1];

            return l[row - 1, col - 1];
        }

    }
}