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 Go (1.6) (judge verdict: Time Limit Exceeded)

package main

import (
	"bufio"
	"fmt"
	"log"
	"os"
	"strconv"
)

// const abcd = "abcdefghijklmnopqrstuvwxyz"
// const ABCD = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"

// var dy = [...]int{1, 1, 0, -1, -1, -1, 0, 1}
// var dx = [...]int{0, 1, 1, 1, 0, -1, -1, -1}

// var dx = [...]int{0, 1, 0, -1}
// var dy = [...]int{1, 0, -1, 0}

var inf int = 1e13
var mod = 1000000007

// ---------------------------------------------------------
func main() {
	log.SetFlags(log.Lshortfile)
	next := newScanner()
	s := next.Line()
	kaib := make([][]bool, len(s)+1)
	for i := 0; i < len(s)+1; i++ {
		kaib[i] = make([]bool, len(s)+1)
	}
	for i := 0; i < len(s); i++ {
		for j := i; j <= len(s); j++ {
			s1 := s[i:j]
			n := len(s[i:j])
			kaib[i][j] = kaibun(s1, n)
		}
	}
	// abc := map[byte]int{}
	// for i := 0; i < len(s); i++ {
	// 	abc[s[i]]++
	// 	cnt := 0
	// 	b := true
	// 	for _, n := range abc {
	// 		if n%2 != 0 && i%2 == 0 {
	// 			b = false
	// 			break
	// 		}
	// 		if n%2 != 0 && i%2 == 1 {
	// 			if cnt > 0 {
	// 				b = false
	// 				break
	// 			}
	// 			cnt++
	// 		}
	// 	}
	// }
	dp := make([]int, len(s)+2)
	// [どこまで分割したか] 分割した時の最小回文数
	for i := 0; i < len(dp); i++ {
		dp[i] = inf
	}
	dp[0] = 0
	dp[1] = 1
	for i := 1; i < len(s)+1; i++ {
		for j := 0; j <= i; j++ {
			// log.Println(i, j, s[j:i], kaibun(s[j:i]))
			if kaib[j][i] {
				// log.Println(dp[i], dp[j])
				dp[i] = min(dp[i], dp[j]+1)
				break
			}

			// log.Println(dp)
		}
	}

	// fmt.Println(dp)
	fmt.Println(dp[len(s)])
}

func kaibun(s string, n int) bool {
	r := true
	if n == 1 {
		return true
	}
	abc := map[byte]int{}
	for i := 0; i < n; i++ {
		abc[s[i]]++
	}
	cnt := 0
	for _, n := range abc {
		if n%2 != 0 {
			cnt++
			if cnt > 1 && n%2 != 0 {
				r = false
			}
			if n%2 == 0 {
				r = false
			}
		}
	}
	return r
}

// ---------------------------------------------------------

// Pair is liked C++ pair
type Pair struct {
	a, b int
}

// Pairs is sorted by []Pair struct
type Pairs []Pair

func (p Pairs) Len() int {
	return len(p)
}
func (p Pairs) Swap(i, j int) {
	p[i], p[j] = p[j], p[i]
}

func (p Pairs) Less(i, j int) bool {
	if p[i].a < p[j].a {
		return true
	} else if p[i].a == p[j].a {
		return p[i].b < p[j].b
	}
	return false
}

// -------------------------------
func in(c, a, z int) bool {
	return c >= a && c < z
}

func btoi(b bool) int {
	if b {
		return 1
	}
	return 0
}

func itob(a int) bool {
	if a == 0 {
		return false
	}
	return true
}

func max(a ...int) int {
	r := a[0]
	for i := 0; i < len(a); i++ {
		if r < a[i] {
			r = a[i]
		}
	}
	return r
}

func sum(a ...int) int {
	r := a[0]
	if len(a) > 1 {
		for i := 1; i < len(a); i++ {
			r += a[i]
		}
	}
	return r
}

func min(a ...int) int {
	r := a[0]
	for i := 0; i < len(a); i++ {
		if r > a[i] {
			r = a[i]
		}
	}
	return r
}

func minmax(a, b int) (int, int) {
	if a > b {
		return b, a
	}
	return a, b
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

// ---------- buffered scanner -----------------------------------------
type scanner struct {
	r   *bufio.Reader
	buf []byte
	p   int
}

func newScanner() *scanner {
	rdr := bufio.NewReaderSize(os.Stdin, 10000)
	return &scanner{r: rdr}
}
func (s *scanner) next() string {
	s.pre()
	start := s.p
	for ; s.p < len(s.buf); s.p++ {
		if s.buf[s.p] == ' ' {
			break
		}
	}
	result := string(s.buf[start:s.p])
	s.p++
	return result
}
func (s *scanner) Line() string {
	s.pre()
	start := s.p
	s.p = len(s.buf)
	return string(s.buf[start:])
}
func (s *scanner) Int() int {
	v, _ := strconv.Atoi(s.next())
	return v
}
func (s *scanner) Int64() int64 {
	v, _ := strconv.ParseInt(s.next(), 10, 64)
	return v
}
func (s *scanner) pre() {
	if s.p >= len(s.buf) {
		s.readLine()
		s.p = 0
	}
}
func (s *scanner) readLine() {
	s.buf = make([]byte, 0)
	for {
		l, p, e := s.r.ReadLine()
		if e != nil {
			panic(e)
		}
		s.buf = append(s.buf, l...)
		if !p {
			break
		}
	}
}