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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace D_After
{
    class Program
    {
        static bool[] CalcHash(string str)
        {
            bool[] ret = new bool[26];
            foreach (var v in str)
            {
                ret[v - 'a'] ^= true;
            }
            return ret;
        }

        static bool IsPalindrome(bool[] a, bool[] b)
        {
            return a.Zip(b, (x, y) => x ^ y).Where(x => x).Count() < 2;
        }

        static int BoolArrayToInt(bool[] b)
        {
            if (b.Length <= 0)
                return 0;
            int ret = 0;
            foreach (var v in b)
            {
                ret <<= 1;
                ret += v ? 1 : 0;
            }
            return ret;
        }

        static bool[] IntToBoolArray(int n)
        {
            bool[] ret = new bool[26];
            for (int i = 25; n > 0 && i >= 0; i--, n /= 2)
            {
                ret[i] = n % 2 == 0 ? false : true;
            }
            return ret;
        }

        static void Main(string[] args)
        {
            string input = Console.ReadLine();
            bool[][] a = new bool[input.Length + 1][];
            for (int i = 0; i < a.Length; i++)
            {
                a[i] = CalcHash(input.Substring(0, i));
            }
            int[] opt = new int[input.Length + 1];

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

            opt[0] = 0;

            List<bool[]> X = new List<bool[]>();
            for (int i = -1; i < 26; i++)
            {
                var v = new bool[26];
                if (i >= 0)
                    v[i] = true;
                X.Add(v);
            }

            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 (IsPalindrome(a[i], a[j]))
                    {
                        s.Add(j);
                    }
                }
                opt[i] = s.Select(x => opt[x]).Min() + 1;
                */

                // O(n) method
                Dictionary<int, List<int>> t = new Dictionary<int, List<int>>();

                int x = BoolArrayToInt(a[i - 1]);
                if (!t.ContainsKey(x))
                {
                    t.Add(x, new List<int>());
                }
                t[x].Add(i - 1);

                foreach (var v in t.Keys)
                {
                    if (!dp.ContainsKey(v))
                        dp.Add(v, int.MaxValue);
                    dp[v] = t[v].Select(y => opt[y]).Union(new int[] { dp[v] }).Min();
                }

                opt[i] = X.Select(y => { var z = BoolArrayToInt(a[i].Zip(y, (f, g) => f ^ g).ToArray()); return dp.ContainsKey(z) ? dp[z] : int.MaxValue; }).Min() + 1;
            }

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