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];
	m = strlen(X);
	n = strlen(Y);
	for(i = 0; i < m; i++){
		a[i][0] = 0;
	}
	for(j = 0; j < n; j++){
		a[0][j] = 0;
	}
	
	for(i = 1; i < m+1; i++){
		for(j = 1; j < n+1; 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];
		}
	}
	
	return a[i-1][j-1];
}

int main(){
	int i, n;
	char x[1001], y[1001];
	
	scanf("%d", &n);
	for(i = 0; i < n; i++){
		scanf("%s", x);
		scanf("%s", y);
		printf("%d\n", LCS(x, y));
		
	}
	
	return 0;
}