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>

int lcs(char x[], char y[])
{
  int i, j, m, n, a[1001][1001], max = 0;

  n = strlen(x);
  m = strlen(y);
  for (i = 0; i <= n; i++)
    a[i][0] = 0;
  for (j = 1; j <= m; j++)
    a[0][j] = 0;
  for (i = 1; i <= n; i++)
    for (j = 1; j <= m; j++){
      if (x[i-1] == y[j-1])
	a[i][j] = a[i-1][j-1]+1;
      else{
	if (a[i-1][j] >= a[i][j-1])
	  a[i][j] = a[i-1][j];
	else
	  a[i][j] = a[i][j-1];
      }
      if (a[i][j] > max)
	max = a[i][j];
    }
  
  return max;
}

int main()
{
  int i, q, c[150];
  char x[1000], y[1000];

  scanf("%d",&q);
  for (i = 0; i < q; i++){
    scanf("%s%s",x,y);
    c[i] = lcs(x,y);
  }
  for (i = 0; i < q; i++)
    printf("%d\n",c[i]);
  
  return 0;
}