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 Python (judge verdict: Time Limit Exceeded)

def count(str1, str2):
    cnt = 0
    count_map = [[0 for j in range(len(str2) + 1)] for i in range(len(str1) + 1)]

    for i in xrange(len(str1)):
        count_map[i][0] = 0
    for j in xrange(len(str2)):
        count_map[0][j] = 0


    for i in xrange(len(str1)):
        for j in xrange(len(str2)):
            if str1[i] == str2[j]:
                count_map[i][j] = count_map[i - 1][j - 1] + 1
            else:
                count_map[i][j] = max(count_map[i - 1][j], count_map[i][j - 1])
        cnt = max(cnt, count_map[i][j])

    return count_map[i][j]

p = input()

for i in xrange(p):
    X = raw_input()
    Y = raw_input()
    ans = count(X, Y)
    print ans