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;
					
public class Program
{	
	public static void Main()
	{
		int n = int.Parse(Console.ReadLine());
		
		for(int i = 0; i < n ; i++) {
			string X = Console.ReadLine();
			string Y = Console.ReadLine();
			
			int[,] DP = new int[X.Length + 1, Y.Length + 1];
			
			for(int j = 1; j < (X.Length + 1); j++) {
				for(int k = 1; k < (Y.Length + 1); k++) {
					DP[j,k] = LCS(DP, j, k, X, Y);
				}
			}
			
			Console.WriteLine(DP[X.Length, Y.Length]);
		}
	}
	
	public static int LCS(int[,] DP, int i, int j, string X, string Y)
	{
		if(X.Substring(i-1,1) == Y.Substring(j-1,1)) return DP[i-1, j-1] + 1;
		else return Math.Max(DP[i-1,j], DP[i,j-1]);
	}
}