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;
class Main{
    final static int  MAX_N = 1500;
    static int[][] memorry = new int[MAX_N][MAX_N];
    public static void main(String[] args){
	Scanner scan = new Scanner(System.in);
	int n;

	n = scan.nextInt();
	for(int i=0; i<n; i++){
	    char[] str1 = scan.next().toCharArray();
	    char[] str2 = scan.next().toCharArray();
	    solve(str1, str2);
	}
    }

    static void solve(char[] str1, char[] str2){
	for(int i=0; i<MAX_N; i++){
	    for(int j=0; j<MAX_N; j++){
		memorry[i][j]=0;
	    }
	}
	for(int i=0; i<str1.length; i++){
	    for(int j=0; j<str2.length; j++){
		if(str1[i]==str2[j])memorry[i+1][j+1]=memorry[i][j]+1;
		else memorry[i+1][j+1]=Math.max(memorry[i][j+1], memorry[i+1][j]);
	    }
	}
	System.out.println(memorry[str1.length][str2.length]);
    }
}