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)

#define _CRT_SECURE_NO_WARNINGS
#include<stdio.h>
#include<stdlib.h>
#include<string.h>

void LCS(char *x, char *y){
	int m = strlen(x+1);
	int n = strlen(y+1);
	int i, j, **c;
	
	c = malloc(sizeof(int)*(2205));
	for (i = 0; i <= m; i++)
		c[i] = malloc(sizeof(int)*(2205));
	
	for (i = 0; i <= m; i++){
		for (j = 0; j <= n; j++){
			c[i][j] = 0;
		}
	}
	
	for (i = 1; i <= m; i++){
		for (j = 1; j <= n; j++){
			if (x[i] == y[j])
				c[i][j] = c[i - 1][j - 1] + 1;
			else if (c[i - 1][j] >= c[i][j - 1])
				c[i][j] = c[i - 1][j];
			else
				c[i][j] = c[i][j - 1];
		}
	}
	
	printf("%d\n", c[i-1][j-1]);
	for (i = 0; i < m; i++)free(c[i]);
	free(c);
	
}

int main(){
	int i, n;
	char x[1001], y[1001];

	scanf("%d", &n);
	for (i = 0; i < n; i++){
		scanf("%s%s", x + 1, y + 1);
		LCS(x, y);
	}
	return 0;
}