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<stdio.h>
#include<string.h>

#define N 1000

int A[N+1][N+1];

int LCS(char *,char *);
int max(int, int);

int main()
{
  int q,i;
  char X[N+1],Y[N+1];

  scanf("%d",&q);
  for(i=0;i<q;i++)
    {
      scanf("%s",X);
      scanf("%s",Y);
      printf("%d\n",LCS(X,Y));
    }
  
  return 0;
}

int LCS(char *X,char *Y)
{
  int i,j,n1,n2;

  n1=strlen(X);
  n2=strlen(Y);

  for(i=1;i<=n1;i++)
    {
      for(j=1;j<=n2;j++)
        {
          if(X[i-1]==Y[j-1])
            {
              A[i][j]=A[i-1][j-1]+1;
            }
          else
            {
              A[i][j]=max(A[i-1][j],A[i][j-1]);
            }
        }
    }
  return A[n1][n2];
}
int max(int a,int b)
{
  if(a>=b)
    return a;
  else
    return b;
}