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;
using System.Linq;
using System.Collections.Generic;
using System.Text;


class C
{
    static int[,] m=new int[101,101];
    static int[] p=new int[101];
    public static void Main() {
        int n = int.Parse(System.Console.ReadLine());
        StringBuilder output = new StringBuilder();
        for (int i = 0; i < n; i++) {
            string x = Console.ReadLine();
            string y = Console.ReadLine();
            output.AppendLine(LCSLength(x, y).ToString());
        }
        Console.Write(output);
    }
    public static int LCSLength(string x, string y) {
        int m = x.Length;
        int n = y.Length;
        x = " " + x;
        y = " " + y;
        int max = 0;
        int[,] c = new int[1001, 1001];
        for(int i = 1; i <= m; i++) {
            for(int j = 1; j <= n; j++) {
                if (x[i] == y[j]) {
                    c[i, j] = c[i - 1, j - 1] + 1;
                }else if (c[i - 1, j] >= c[i, j - 1]) {
                    c[i, j] = c[i - 1, j];
                } else {
                    c[i, j] = c[i, j - 1];
                }
                max = Math.Max(max, c[i, j]);
            }
        }
        return max;
    }
}