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 + 10)
#define max(a,b)(a<b?b:a)

int dp[N][N];
char a[N],b[N];

int lcs(void)
{
  const int a_size=strlen(a)-1;
  const int b_size=strlen(b)-1;

  int i,j;

  memset(dp,0,sizeof(dp));

  for(i=1;i<a_size+1;++i)
    {
      for(j=1;j<b_size+1;++j)
	{
	  int mx =max(dp[i][j-1],dp[i-1][j]);
	  if(a[i-1]==b[j-1])
	    {
	      mx=max(mx,dp[i-1][j-1]+1);
	    }
	  dp[i][j]=mx;
	}
    }
  return dp[a_size][b_size];
}

int main()
{
  int n,i;
  scanf("%d\n",&n);

  for(i=0;i<n;i++)
    {
      fgets(a,N,stdin);
      fgets(b,N,stdin);
      printf("%d\n",lcs());
    }

  return 0;
}