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.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace lec10C
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            for (int i = 0; i < n; i++)
            {
                string  x = Console.ReadLine();
                string  y = Console.ReadLine();
                int output = LCSsolve(x, y);
                Console.WriteLine(output);
            }

            Console.ReadLine();

        }

        static int LCSsolve(string x, string y)
        {
            int m = x.Length;
            int n = y.Length;
            int[,] arr = new int[m + 1, n+1] ;

            for (int i = 1; i <= m; i++)
            {
                arr[i, 0] = 0;
            }

            for (int j = 0; j <= n; j++)
            {
                arr[ 0 , j] = 0;
            }

            for (int i = 1; i <= m; i++)
            {
                for (int  j = 1; j <= n; j++)
                {
                    if (x[i-1] == y[j-1])
                    {
                        arr[i, j] = arr[i - 1, j - 1] + 1;
                    } else if ( arr[i-1 , j ] >= arr[i, j - 1])
                    {
                        arr[i, j] = arr[i-1,j];
                    }
                    else
                    {
                        arr[i, j] = arr[i,j-1];
                    }
                }
            }

            return arr[m,n];
        }

    }
}