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 Go (judge verdict: Accepted)

package main

import "fmt"

func main() {
	var nPairs int
	fmt.Scanln(&nPairs)

	var a, b string
	for i := 0; i < nPairs; i++ {
		fmt.Scanln(&a)
		fmt.Scanln(&b)
		fmt.Println(lcsSize(a, b))
	}
}

func lcsSize(sa, sb string) int {
	dp := make([][]int, len(sa)+1)
	for i := 0; i <= len(sa); i++ {
		dp[i] = make([]int, len(sb)+1)
	}

	for a := 1; a <= len(sa); a++ {
		for b := 1; b <= len(sb); b++ {
			if sa[a-1] == sb[b-1] {
				dp[a][b] = dp[a-1][b-1] + 1
			} else {
				dp[a][b] = max(dp[a][b-1], dp[a-1][b])
			}
		}
	}

	return dp[len(sa)][len(sb)]
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}