Question
Research Notes Alignment

Two researchers typed notes about the same experiment, but both skipped some words while summarizing. Each note is represented as a lowercase string. A common trace is a sequence of characters that appears in both notes in the same relative order, not necessarily continuously.

Find the length of the longest common trace.

The twist: matching characters do not need to be adjacent, but their order must be preserved.

Input

The first line contains a string KaTeX can only parse string typed expression.

The second line contains a string KaTeX can only parse string typed expression.

Output

Print a single integer — the length of the longest common trace.

Example
Example 1:
Input
abcde

ace
Output
3
Explanation
The sequence KaTeX can only parse string typed expression appears in both strings.

Example 2:
Input
training

rating
Output
5

Online