Longest common subsequence

Print the length of the longest sequence of characters that appears in both strings in the same order (not necessarily next to each other).

Reported in: LTIMindtree (memory-based)

Input

Two lines, one string each.

Output

The length.

Constraints

1 ≤ length ≤ 1000.

Example 1

Input:
ABCBDAB
BDCABA

Output:
4

Example 2

Input:
abc
def

Output:
0

Hint: dp[i][j] = dp[i−1][j−1] + 1 when the characters match, otherwise the larger of dp[i−1][j] and dp[i][j−1].

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