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>
void LCS(char *,char *);
int main(){
  int n,i,j,k[5],l,m;
  char a[1030][1030],b[1030][1030];
  
  scanf("%d",&n);
  for(i=1;i<=n;i++){
    scanf("%s",a[i]);
    scanf("%s",b[i]);
  }
    for(i=1;i<=n;i++){
      LCS(a[i],b[i]);
    }
    return 0;
}
void LCS(char *a,char *b){
  int m,l,n,i,j,c[1030][1030];
  m=strlen(a);
  l=strlen(b);
  for(i=1;i<=m;i++){
    for(j=1;j<=l;j++){
      c[i][j]=0;
    }
  }
  for(i=1;i<=m;i++){
    for(j=1;j<=l;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];
      }
    }
  }
  printf("%d\n",c[m][l]);
}