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;
using ll  = long long;
using vl  = vector<ll>;
using vvl = vector<vl>;
#define rng(i,a,b) for(int i = (a); i < (b); ++i)
#define rep(i,n) for(int i = 0; i < (n); ++i)
#define DEBUG(x) cerr<<__LINE__<<": "<<#x<<" = "<<x<<"\n"
const int INF = 1e9;

int N;
vvl alnumf, alnumb;

bool isPalindrome(vl alnum) {
    int sum = 0;
    rep(i,26) sum += alnum[i] % 2;
    return sum <= 1;
}

vl getAlnum(int l, int r) {
    vl alnum(26, 0);
    rep(i,26) {
        alnum[i] += (l < r ? alnumf[r][i]-alnumf[l][i] : alnumb[l][i]-alnumb[r][i]);
        // if (i > 4) continue;
        // DEBUG((char)('a'+i));
        // DEBUG(alnum[i]);
    }
    return alnum;
}

bool isPalindrome(int l, int r) {
    return isPalindrome(getAlnum(l, r));
}

int main() {
    string s; cin >> s;
    N = s.length();
    alnumf.assign(N+1, vl(26, 0));
    alnumb.assign(N+1, vl(26, 0));
    rep(i,N) {
        int cf = s[i] - 'a';
        int cb = s[N-i-1] - 'a';
        alnumf[i+1][cf]++;
        alnumb[i+1][cb]++;
        rep(j,26) {
            alnumf[i+1][j] += alnumf[i][j];
            alnumb[i+1][j] += alnumb[i][j];
        }
    }
    vl dp(N+1, INF);
    dp[0] = 0;
    rng(r,1,N+1) {
        rep(l,r) {
            if (isPalindrome(l, r)) {
                dp[r] = min(dp[r], dp[l] + 1);
            }
        }
    }
    cout << dp[N] << endl;
    return 0;
}