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, c[1002][1002];
    
    m = strlen(x);
    n = strlen(y);
 
    for(i = 0; i <= m; i++){
        for(j = 0; j <= n; j++){
            if(i == 0 || j == 0) c[i][j] = 0;
            if(x[i] == y[j]) c[i+1][j+1] = c[i][j] + 1;
            else if(c[i][j+1] >= c[i+1][j]) c[i+1][j+1] = c[i][j+1];
            else c[i+1][j+1] = c[i+1][j];
        }
    }
    
    return c[m][n];
  
}

int main(){
    
    char x[1002], y[1002];
    int i, q;
    
    scanf("%d", &q);
    
    while(q--){
        scanf("%s%s", x, y);
        printf("%d\n", LCS(x, y));
    }
   
    return 0;
    
}