Problem:
Score : 700 points

Problem Statement

We have a string s consisting of lowercase English letters.
Snuke is partitioning s into some number of non-empty substrings.
Let the subtrings obtained be s_1, s_2, ..., s_N from left to right. (Here, s = s_1 + s_2 + ... + s_N holds.)
Snuke wants to satisfy the following condition:

For each i (1 \leq i \leq N), it is possible to permute the characters in s_i and obtain a palindrome.

Find the minimum possible value of N when the partition satisfies the condition.

Constraints

1 \leq |s| \leq 2 \times 10^5

s consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

s

Output

Print the minimum possible value of N when the partition satisfies the condition.

Sample Input 1

aabxyyzz

Sample Output 1

2

The solution is to partition s as aabxyyzz = aab + xyyzz.
Here, aab can be permuted to form a palindrome aba, and xyyzz can be permuted to form a palindrome zyxyz.

Sample Input 2

byebye

Sample Output 2

1

byebye can be permuted to form a palindrome byeeyb.

Sample Input 3

abcdefghijklmnopqrstuvwxyz

Sample Output 3

26

Sample Input 4

abcabcxabcx

Sample Output 4

3

The solution is to partition s as abcabcxabcx = a + b + cabcxabcx.

Solution in Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

#!/usr/bin/env ruby

class String
  def has_kaibunability?
    [0, 1].include? self.strip.chars.group_by(&:itself).values.map(&:size).reject(&:even?).size
  end
end

s = gets.strip

@hunko = {}
def unko(s)
  @hunko[s.chars.sort.chunk(&:itself).map(&:last)] ||= if s.has_kaibunability?
    1
  else
    (1..(s.size - 1)).to_a.sort_by { |k| k - s.size / 2 }.map { |sp|
      (unko(s[0..(sp - 1)]) + unko(s[sp..-1])).tap { |k| return 2 if k == 2 }
    }.min
  end
end

puts unko(s)