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)

#include<iostream>
#include<string>

int main(){
  int n;
  std::string x,y;
  std::cin>>n;
  int a[1001][1001];
  int b[n];

  for(int i=0;i<n;i++){
    std::cin>>x;
    std::cin>>y;
    for(int j=0;j<1001;j++){
      for(int k=0;k<1001;k++){
	a[j][k]=0;
      }
    }
    for(int j=1;j<=x.size();j++){
      for(int k=1;k<=y.size();k++){
	if(x[j-1]==y[k-1]){
	  a[j][k]=a[j-1][k-1]+1;
	}else{
	  if(a[j-1][k]>a[j][k-1]){
	    a[j][k]=a[j-1][k];
	  }else{
	    a[j][k]=a[j][k-1];
	  }
	}
      }
    }
    b[i]=a[x.size()][y.size()];
  }

  for(int i=0;i<n;i++){
  std::cout<<b[i]<<"\n";
  }

  return 0;
}