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: Time Limit Exceeded)

using System;

class Program{
    static int[,] memo;

    static int Count(string X, int x, string Y, int y, bool flag){
        if (flag) {
            if (memo[x, y]!=-1) {
                return memo[x, y];
            }
        } else {
            if (memo[y, x]!=-1) {
                return memo[y, x];
            }
        }
        var max=0;
        for (var xbegin=x; xbegin<X.Length; xbegin++) {
            for (var yi=y; yi<Y.Length; yi++) {
                if (X[xbegin]==Y[yi]) {
                    var tmp=Count(Y, yi+1, X, xbegin+1, !flag)+1;
                    if (tmp>max) {
                        max=tmp;
                    }
                    break;
                }
            }
        }

        if (flag) {
            memo[x, y]=max;
            return memo[x, y];
        } else {
            memo[y, x]=max;
            return memo[y, x];
        }
    }


    public static void Main(){
        var q=int.Parse(Console.ReadLine());
        for (var i=0; i<q; i++) {
            var X=Console.ReadLine();
            var Y=Console.ReadLine();
            memo=new int[X.Length+1, Y.Length+1];
            for (var x=0; x<X.Length; x++) {
                for (var y=0; y<Y.Length; y++) {
                    memo[x, y]=-1;
                }
            }
            Console.WriteLine(Count(X, 0, Y, 0, true));
        }
    }
}