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 JAVA (judge verdict: Accepted)

import java.util.Scanner;

public class Main{
	
	public static int max(int x, int y) {
		if(x > y)
			return x;
		else return y;
	}
	
	public static int longest(String x, String y) {
		int[][] results = new int[x.length()+1][y.length()+1];
		int max = 0;
		for(int i = 0; i <= x.length(); i++) {
			for(int j = 0; j <= y.length(); j++) {
				if(i == 0 || j == 0)
					results[i][j] = 0;
				else if(x.charAt(i-1) == y.charAt(j-1))
					results[i][j] = results[i-1][j-1] + 1;
				else results[i][j] = max(results[i-1][j], results[i][j-1]);
				if(results[i][j] > max)
					max = results[i][j];
			}
		}
		return max;
	}
	
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int limit = in.nextInt();
		for(int i = 0; i < limit; i++) {
			System.out.println(longest(in.next(), in.next()));
		}
		in.close();
	}

}