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 MAX 1002
int lcs[MAX][MAX];

int max(int a,int b){
  if(a > b){
    return a;
  }
  else return b;
}

int lcscheck(char a[],char b[]){
  int i,j,ans =0;
  int al = strlen(a);
  int bl = strlen(b);
  for(j=1;j<bl;j++)
  for(i=1;i<al;i++){
    if(a[i] == b[j]){
      lcs[i][j] = lcs[i-1][j-1] + 1;
    }else{
      if(lcs[i][j-1] > lcs[i-1][j])lcs[i][j] = lcs[i][j-1];
      else lcs[i][j] = lcs[i-1][j];
    }
    ans = max(lcs[i][j],ans);
  }
  return ans;
}

int main(){
  int datanum,temp;
  char dataA[MAX+1];
  char dataB[MAX+1];
  char tempdata[MAX];
  scanf(" %d",&datanum);
  for(int i=0;i<datanum;i++){
    scanf(" %s",tempdata);
    strcpy(dataA," ");
    strcat(dataA,tempdata);
    scanf(" %s",tempdata);
    strcpy(dataB," ");
    strcat(dataB,tempdata);
    // printf("%s\n%s\n",dataA,dataB);
    printf("%d\n",lcscheck(dataA,dataB));
  }
  return 0;
}