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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

namespace D_After
{
    class Program
    {
        static void Main(string[] args)
        {
            string input = Console.ReadLine();
            int[] a = new int[input.Length + 1];
            a[0] = 0;
            for (int i = 1; i < a.Length; i++)
                a[i] = a[i - 1] ^ (1 << (input[i - 1] - 'a'));

            int[] opt = new int[input.Length + 1];

            Dictionary<int, int> dp = new Dictionary<int, int>();

            opt[0] = 0;

            List<int> X = new List<int>();
            for (int i = -1; i < 26; i++)
            {
                if (i < 0)
                    X.Add(0);
                else
                    X.Add(1 << i);
            }

            Dictionary<int, List<int>> T = new Dictionary<int, List<int>>();

            for (int i = 1; i <= input.Length; i++)
            {
                /*
                // O(n^2) method
                List<int> s = new List<int>();
                for (int j = 0; j < i; j++)
                    if ((a[i] ^ a[j]) == 0 ? true : ((a[i] ^ a[j]) & ((a[i] ^ a[j]) - 1)) == 0)
                        s.Add(j);
                opt[i] = s.Select(x => opt[x]).Min() + 1;
                */

                // O(n) method
                if (!dp.ContainsKey(a[i - 1]))
                    dp.Add(a[i - 1], int.MaxValue);
                dp[a[i - 1]] = dp[a[i - 1]] <= opt[i - 1] ? dp[a[i - 1]] : opt[i - 1];
                opt[i] = X.Select(x => dp.ContainsKey(a[i] ^ x) ? dp[a[i] ^ x] : int.MaxValue).Min() + 1;
            }

            Console.WriteLine(opt[opt.Length - 1]);
# if DEBUG
            Console.ReadKey();
#endif
        }
    }
}