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++14 (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;

int dp[1010][1010];

int main()
{
  int q;
  string x,y;

  cin >> q;

  for(int t = 0;t < q;t++){
    cin >> x;
    cin >> y;

    memset(dp, 0, sizeof(dp));
    
    for(int i = 1;i <= x.size();i++){
      for(int j = 1;j <= y.size();j++){

	if(x[i-1] == y[j-1]){
	  dp[i][j] = dp[i-1][j-1]+1;
	}
	else if(dp[i-1][j] <= dp[i][j-1]){
	  dp[i][j] = dp[i][j-1];
	}
	else{
	  dp[i][j] = dp[i-1][j];
	}
      }
    }
    cout << dp[x.size()][y.size()] << endl;
  }
  return 0;
}