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++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0;i<int(n);++i)
#define INF 1e9

multimap<int,int> mp;
vector<int> bit;
vector<int> dp;

void update(int v,int state){
    auto p = mp.equal_range(state);
    for (auto it = p.first; it != p.second; ++it) {
        int next = it->second;
        if(v<next) {
            dp[next] = min(dp[next],dp[v]+1);
        }
    }
}

int main(void){
    string s;
    cin>>s;
    int N = s.size();
    bit = vector<int>(N+1);
    dp = vector<int>(N+1,INF);
    dp[0] = 0;
    rep(i,N){
        bit[i+1] = bit[i]^(1<<(s[i]-'a'));
        mp.insert(make_pair(bit[i+1],i+1));
    }

    rep(i,N){
        update(i,bit[i]);
        rep(j,26){
            update(i,bit[i]^(1<<j));
        }
    }
    cout<<dp[N]<<endl;

    return 0;
}