| # 156_A. Message |
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| ## Problem Description |
| Dr. Moriarty is about to send a message to Sherlock Holmes. He has a string s. |
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| String p is called a substring of string s if you can read it starting from some position in the string s. For example, string "aba" has six substrings: "a", "b", "a", "ab", "ba", "aba". |
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| Dr. Moriarty plans to take string s and cut out some substring from it, let's call it t. Then he needs to change the substring t zero or more times. As a result, he should obtain a fixed string u (which is the string that should be sent to Sherlock Holmes). One change is defined as making one of the following actions: |
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| * Insert one letter to any end of the string. |
| * Delete one letter from any end of the string. |
| * Change one letter into any other one. |
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| Moriarty is very smart and after he chooses some substring t, he always makes the minimal number of changes to obtain u. |
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| Help Moriarty choose the best substring t from all substrings of the string s. The substring t should minimize the number of changes Moriarty should make to obtain the string u from it. |
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| Input |
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| The first line contains a non-empty string s, consisting of lowercase Latin letters. The second line contains a non-empty string u, consisting of lowercase Latin letters. The lengths of both strings are in the range from 1 to 2000, inclusive. |
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| Output |
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| Print the only integer — the minimum number of changes that Dr. Moriarty has to make with the string that you choose. |
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| Examples |
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| Input |
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| aaaaa |
| aaa |
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| Output |
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| 0 |
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| Input |
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| abcabc |
| bcd |
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| Output |
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| 1 |
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| Input |
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| abcdef |
| klmnopq |
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| Output |
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| 7 |
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| Note |
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| In the first sample Moriarty can take any substring of length 3, and it will be equal to the required message u, so Moriarty won't have to make any changes. |
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| In the second sample you should take a substring consisting of characters from second to fourth ("bca") or from fifth to sixth ("bc"). Then you will only have to make one change: to change or to add the last character. |
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| In the third sample the initial string s doesn't contain any character that the message should contain, so, whatever string you choose, you will have to make at least 7 changes to obtain the required message. |
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| ## Contest Information |
| - **Contest ID**: 156 |
| - **Problem Index**: A |
| - **Points**: 500.0 |
| - **Rating**: 1700 |
| - **Tags**: brute force |
| - **Time Limit**: {'seconds': 2, 'nanos': 0} seconds |
| - **Memory Limit**: 256000000 bytes |
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| ## Task |
| Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases. |
