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 {

	static int lcs(String left,String right){

		int left_len = left.length();
		int right_len = right.length();

		int dp[][] = new int[left_len+1][right_len+1];

		for(int i = 0; i <= left_len; i++){
			for(int k = 0; k <= right_len; k++){
				dp[i][k] = 0;
			}
		}

		for(int i = 0; i < left_len; i++){
			for(int k = 0; k < right_len; k++){
				if(left.charAt(i) == right.charAt(k)){
					dp[i+1][k+1] = dp[i][k]+1;
				}else{
					dp[i+1][k+1] = Math.max(dp[i+1][k], dp[i][k+1]);
				}
			}
		}

		return dp[left_len][right_len];
	}

	public static void main(String args[]){

		Scanner sc = new Scanner(System.in);

		int N = Integer.parseInt(sc.nextLine());

		String left,right;

		for(int i = 0; i < N; i++){
			left = sc.nextLine();
			right = sc.nextLine();

			System.out.printf("%d\n", lcs(left,right));
		}
	}
}