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 lcs(char *, char *);
int isHigher(int, int);

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

  scanf("%d",&q);

  for(i = 0; i < q; i++){
    scanf("%s %s",&X[1],&Y[1]);
    X[0] = Y[0] = ' ';
    ret = lcs(X,Y);
    printf("%d\n",ret);
  }
  
  return 0;
}

int lcs(char X[], char Y[])
{
  int c[N+1][N+1];
  int m,n,maxl = 0,i,j;

  m = strlen(X)-1;
  n = strlen(Y)-1;

  X[0] = ' ';
  Y[0] = ' ';

  for(i = 0; 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(X[i] == Y[j]){
	c[i][j] = c[i-1][j-1] + 1;
      }else c[i][j] = isHigher(c[i][j-1],c[i-1][j]);
      maxl = isHigher(maxl,c[i][j]);
    }
  }

    return maxl;
}

int isHigher(int x, int y)
{
  if(x >= y)return x;
  else return y;
}