Edit Distance (Levenshtein Distance)

Find the edit distance between given two words s1 and s2.

The disntace is the minimum number of single-character edits required to change one word into the other. The edits including the following operations:

• insertion: Insert a character at a particular position.
• deletion: Delete a character at a particular position.
• substitution: Change the character at a particular position to a different character

Constraints

• 1 ≤ length of s1 ≤ 1000
• 1 ≤ length of s2 ≤ 1000

Input

s1 s2

Two words s1 and s2 are given in the first line and the second line respectively. The words will consist of lower case characters.

Output

Print the edit distance in a line.

Examples

Input

acac acm

Output

2

Input

icpc icpc

Output

0

inputFormat

Input

s1 s2

Two words s1 and s2 are given in the first line and the second line respectively. The words will consist of lower case characters.

outputFormat

Output

Print the edit distance in a line.

Examples

Input

acac acm

Output

2

Input

icpc icpc

Output

0

样例

icpc
icpc

0