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 Rust (1.15.1) (judge verdict: Memory Limit Exceeded)

use self::mod_int::ModInt;
use std::cmp;
use std::collections::BinaryHeap;

const MOD: usize = 1e9 as usize + 7;
const INF: i64 = 1 << 60;

fn main() {
    let (r, w) = (std::io::stdin(), std::io::stdout());
    let mut sc = IO::new(r.lock(), w.lock());

    let s = sc
        .read::<String>()
        .chars()
        .map(|c| c as usize - 'a' as usize)
        .collect::<Vec<_>>();
    let mut prefix_set = vec![INF; 1 << 26];
    prefix_set[0] = 0;
    let mut cur: usize = 0;
    for s in s.into_iter() {
        cur ^= 1 << s;
        let mut min = INF;
        if cur.count_ones() <= 1 {
            min = 1;
        }
        for i in 0..26 {
            let suffix = 1 << i;
            let prefix = cur ^ suffix;
            min = cmp::min(min, prefix_set[prefix] + 1);
        }
        prefix_set[cur] = min;
    }

    println!("{}", prefix_set[cur]);
}
pub mod range_add_segment_tree {

    pub struct RangeAddSegmentTree<T, F> {
        seg: Vec<T>,
        seg_add: Vec<T>,
        num: usize,
        f: F,
        init: T,
    }

    impl<T, F> RangeAddSegmentTree<T, F>
    where
        T: PartialOrd + ::std::ops::Add<Output = T> + ::std::ops::Sub<Output = T> + Copy,
        F: Fn(T, T) -> T,
    {
        pub fn new(n: usize, init: T, f: F, zero: T) -> Self {
            let num = n.next_power_of_two();
            RangeAddSegmentTree {
                seg: vec![init; num * 2],
                seg_add: vec![zero; num * 2],
                num: num,
                init: init,
                f: f,
            }
        }

        /// add to [a, b)
        pub fn add(&mut self, a: usize, b: usize, value: T) {
            let num = self.num;
            self.add_to_range(a, b, value, 0, 0, num);
        }

        fn add_to_range(
            &mut self,
            a: usize,
            b: usize,
            value: T,
            mut k: usize,
            left: usize,
            right: usize,
        ) {
            if b <= left || right <= a {
                return;
            }
            if a <= left && right <= b {
                self.seg_add[k] = self.seg_add[k] + value;
                while k > 0 {
                    k = (k - 1) / 2;
                    self.seg[k] = (self.f)(
                        self.seg[k * 2 + 1] + self.seg_add[k * 2 + 1],
                        self.seg[k * 2 + 2] + self.seg_add[k * 2 + 2],
                    );
                }
            } else {
                self.add_to_range(a, b, value, k * 2 + 1, left, (left + right) / 2);
                self.add_to_range(a, b, value, k * 2 + 2, (left + right) / 2, right);
            }
        }

        pub fn update(&mut self, pos: usize, value: T) {
            let cur = self.get(pos, pos + 1);
            let mut k = pos + self.num - 1;
            let raw = self.seg[k];
            self.seg[k] = raw + value - cur;
            while k > 0 {
                k = (k - 1) / 2;
                self.seg[k] = (self.f)(self.seg[k * 2 + 1], self.seg[k * 2 + 2]);
            }
        }

        pub fn get(&self, a: usize, b: usize) -> T {
            self.get_from_range(a, b, 0, 0, self.num)
        }

        fn get_from_range(&self, a: usize, b: usize, k: usize, left: usize, right: usize) -> T {
            if b <= left || right <= a {
                self.init
            } else if a <= left && right <= b {
                self.seg[k] + self.seg_add[k]
            } else {
                let mid = (left + right) / 2;
                let x = self.get_from_range(a, b, k * 2 + 1, left, mid);
                let y = self.get_from_range(a, b, k * 2 + 2, mid, right);
                (self.f)(x, y) + self.seg_add[k]
            }
        }
    }
}
pub mod mod_int {
    use super::MOD;
    use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Sub, SubAssign};

    type Num = usize;

    #[derive(Clone, Copy)]
    pub struct ModInt<T: Copy + Clone>(pub T);

    impl Add<ModInt<Num>> for ModInt<Num> {
        type Output = ModInt<Num>;
        fn add(self, rhs: ModInt<Num>) -> ModInt<Num> {
            self + rhs.0
        }
    }

    impl Add<Num> for ModInt<Num> {
        type Output = ModInt<Num>;
        fn add(self, mut rhs: Num) -> ModInt<Num> {
            if rhs >= MOD {
                rhs %= MOD;
            }
            let mut t = rhs + self.0;
            if t >= MOD {
                t = t - MOD;
            }
            ModInt(t)
        }
    }

    impl Sub<Num> for ModInt<Num> {
        type Output = ModInt<Num>;
        fn sub(self, rhs: Num) -> ModInt<Num> {
            let rhs = if rhs >= MOD { rhs % MOD } else { rhs };
            let value = if self.0 < rhs { self.0 + MOD } else { self.0 };
            ModInt(value - rhs)
        }
    }

    impl Sub<ModInt<Num>> for ModInt<Num> {
        type Output = ModInt<Num>;
        fn sub(self, rhs: ModInt<Num>) -> ModInt<Num> {
            self - rhs.0
        }
    }

    impl AddAssign<Num> for ModInt<Num> {
        fn add_assign(&mut self, other: Num) {
            *self = *self + other;
        }
    }
    impl AddAssign<ModInt<Num>> for ModInt<Num> {
        fn add_assign(&mut self, other: ModInt<Num>) {
            *self = *self + other;
        }
    }

    impl SubAssign<Num> for ModInt<Num> {
        fn sub_assign(&mut self, other: Num) {
            *self = *self - other;
        }
    }

    impl SubAssign<ModInt<Num>> for ModInt<Num> {
        fn sub_assign(&mut self, other: ModInt<Num>) {
            *self = *self - other;
        }
    }

    impl Div<Num> for ModInt<Num> {
        type Output = ModInt<Num>;
        fn div(self, mut rhs: Num) -> ModInt<Num> {
            if rhs >= MOD {
                rhs %= MOD;
            }
            self * ModInt(rhs).pow(MOD - 2)
        }
    }

    impl Div<ModInt<Num>> for ModInt<Num> {
        type Output = ModInt<Num>;
        fn div(self, rhs: ModInt<Num>) -> ModInt<Num> {
            self / rhs.0
        }
    }

    impl DivAssign<Num> for ModInt<Num> {
        fn div_assign(&mut self, rhs: Num) {
            *self = *self / rhs
        }
    }
    impl DivAssign<ModInt<Num>> for ModInt<Num> {
        fn div_assign(&mut self, rhs: ModInt<Num>) {
            *self = *self / rhs
        }
    }

    impl Mul<ModInt<Num>> for ModInt<Num> {
        type Output = ModInt<Num>;

        fn mul(self, rhs: ModInt<Num>) -> ModInt<Num> {
            self * rhs.0
        }
    }
    impl Mul<Num> for ModInt<Num> {
        type Output = ModInt<Num>;

        fn mul(self, mut rhs: Num) -> ModInt<Num> {
            if rhs >= MOD {
                rhs %= MOD;
            }
            let t = (self.0 * rhs) % MOD;
            ModInt(t)
        }
    }

    impl MulAssign<Num> for ModInt<Num> {
        fn mul_assign(&mut self, rhs: Num) {
            *self = *self * rhs;
        }
    }

    impl MulAssign<ModInt<Num>> for ModInt<Num> {
        fn mul_assign(&mut self, rhs: ModInt<Num>) {
            *self = *self * rhs;
        }
    }

    impl ModInt<Num> {
        pub fn pow(self, e: Num) -> ModInt<Num> {
            let mut result = ModInt(1);
            let mut cur = self;
            let mut e = e;
            while e > 0 {
                if e & 1 == 1 {
                    result *= cur;
                }
                e >>= 1;
                cur *= cur;
            }
            result
        }
    }
}
pub struct IO<R, W: std::io::Write>(R, std::io::BufWriter<W>);

impl<R: std::io::Read, W: std::io::Write> IO<R, W> {
    pub fn new(r: R, w: W) -> Self {
        IO(r, std::io::BufWriter::new(w))
    }
    pub fn write<S: ToString>(&mut self, s: S) {
        use std::io::Write;
        self.1.write(s.to_string().as_bytes()).unwrap();
    }
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .0
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r' || b == b'\t')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r' && b != b'\t')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}