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 YOSHI 1000

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

int lcs(char *X,char *Y){
    int c[YOSHI + 1][YOSHI + 1];
    int x,y,i,j,maxl = 0;
    
    x = strlen(X);
    y = strlen(Y);
    
    for(i = 0;i <= x;i++) c[i][0] = 0;
    for(j = 1;j <= y;j++) c[0][j] = 0;
    
    for(i = 1;i <= x;i++){
        for(j = 1;j <= y;j++){
            if(X[i - 1] == Y[j - 1]) c[i][j] = c[i - 1][j - 1] + 1;
            else c[i][j] = max(c[i - 1][j],c[i][j - 1]);
            maxl = max(maxl,c[i][j]);
        }
    }
    
    return maxl;
}

int main(){
    int n,i;
    
    char X[YOSHI],Y[YOSHI];
    
    scanf("%d",&n);
    
    for(i = 0;i < n;i++){
        scanf("%s",X);
        scanf("%s",Y);
        printf("%d\n",lcs(X,Y));
    }
}