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: Wrong Answer)

#include <stdio.h>
#include <string.h>
#define MAX 1000

int lcs(char *,char *);

int main(){
  int n,i;
  char A[MAX+1],B[MAX+1];
  
  scanf("%d",&n);

  for(i=0;i<n;i++){
    //A[0]=' ';
    // B[0]=' ';
    scanf("%s",A);
    scanf("%s",B);
    printf("%d\n",lcs(A,B));
  }
  return 0;
}

int lcs(char *A,char *B){
  int m,n,i,j;
  char C[MAX+1][MAX+1];

  int max=0;
  
  m=strlen(A);
  n=strlen(B);
  
  for(i=1;i<=m;i++){
    C[i][0]=0;
  }
  for(j=1;j<=n;j++){
    C[0][j]=0;
  }
  for(i=1;i<=m;i++){
    for(j=1;j<=n;j++){
      if(A[i-1]==B[j-1]){
	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];
        if(C[i][j]>max) max= C[i][j];

    }
    //  if(C[i][j]>max) max= C[i][j];

  }
  // if(C[m-1][n-1]>max) max= C[m-1][n-1];
  return max;
}