Minimize String Length

Given a string s, you have two types of operation:

Choose an index i in the string, and let c be the character in position i. Delete the closest occurrence of c to the left of i (if exists).
Choose an index i in the string, and let c be the character in position i. Delete the closest occurrence of c to the right of i (if exists).

Your task is to minimize the length of s by performing the above operations zero or more times.

Return an integer denoting the length of the minimized string.

Example 1:

Input: s = "aaabc"

Output: 3

Explanation:

Operation 2: we choose i = 1 so c is 'a', then we remove s[2] as it is closest 'a' character to the right of s[1].
s becomes "aabc" after this.
Operation 1: we choose i = 1 so c is 'a', then we remove s[0] as it is closest 'a' character to the left of s[1].
s becomes "abc" after this.

Example 2:

Input: s = "cbbd"

Output: 3

Explanation:

Operation 1: we choose i = 2 so c is 'b', then we remove s[1] as it is closest 'b' character to the left of s[1].
s becomes "cbd" after this.

Example 3:

Input: s = "baadccab"

Output: 4

Explanation:

Operation 1: we choose i = 6 so c is 'a', then we remove s[2] as it is closest 'a' character to the left of s[6].
s becomes "badccab" after this.
Operation 2: we choose i = 0 so c is 'b', then we remove s[6] as it is closest 'b' character to the right of s[0].
s becomes "badcca" fter this.
Operation 2: we choose i = 3 so c is 'c', then we remove s[4] as it is closest 'c' character to the right of s[3].
s becomes "badca" after this.
Operation 1: we choose i = 4 so c is 'a', then we remove s[1] as it is closest 'a' character to the left of s[4].
s becomes "bdca" after this.

Constraints:

Problem