Problem:
Score : 400 points

Problem Statement

We have a string s consisting of lowercase English letters.
Snuke can perform the following operation repeatedly:

Insert a letter x to any position in s of his choice, including the beginning and end of s.

Snuke's objective is to turn s into a palindrome.
Determine whether the objective is achievable. If it is achievable, find the minimum number of operations required.

Notes

A palindrome is a string that reads the same forward and backward.
For example, a, aa, abba and abcba are palindromes, while ab, abab and abcda are not.

Constraints

1 \leq |s| \leq 10^5

s consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

s

Output

If the objective is achievable, print the number of operations required.
If it is not, print -1 instead.

Sample Input 1

xabxa

Sample Output 1

2

One solution is as follows (newly inserted x are shown in bold):

xabxa → xaxbxa → xaxbxax

Sample Input 2

ab

Sample Output 2

-1

No sequence of operations can turn s into a palindrome.

Sample Input 3

a

Sample Output 3

0

s is a palindrome already at the beginning.

Sample Input 4

oxxx

Sample Output 4

3

One solution is as follows:

oxxx → xoxxx → xxoxxx → xxxoxxx

Solution in Go (1.14.1) (judge verdict: Accepted)

package main

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

var (
	finv, inv, fac [MAX]int
)

func COM(n, k int) int {
	MOD := int(MOD)
	if n < k {
		return 0
	}
	if n < 0 || k < 0 {
		return 0
	}
	return fac[n] * (finv[k] * finv[n-k] % MOD) % MOD
}

func init() {
	MOD := int(MOD)
	fac[0] = 1
	fac[1] = 1
	finv[0] = 1
	finv[1] = 1
	inv[1] = 1
	for i := 2; i < MAX; i++ {
		fac[i] = fac[i-1] * i % MOD
		inv[i] = MOD - inv[MOD%i]*(MOD/i)%MOD
		finv[i] = finv[i-1] * inv[i] % MOD
	}
	//sc.Split(bufio.ScanLines)
	sc.Split(bufio.ScanWords)
	sc.Buffer([]byte{}, 500100)
}

const (
	MAX = 510000
)

var MOD int64 = 1000000007

func ModAdd(a, b int64) int64 {
	return (a + b) % MOD
}

func ModMul(a, b int64) int64 {
	ans := a * b % MOD
	if ans < 0 {
		ans += MOD
	}
	return ans
}

func ModSub(a, b int64) int64 {
	r := (a%MOD - b%MOD) % MOD
	if r < 0 {
		r += MOD
	}
	return r
}

func ModDiv(a, b int64) int64 {
	return a % MOD * ModInv(b) % MOD
}

func ModPow(a, n int64) int64 {
	var r int64 = 1
	for n > 0 {
		if n&1 == 1 {
			r = r * a % MOD
		}
		a = a * a % MOD
		n >>= 1
	}
	return r
}

func ModInv(a int64) int64 {
	var b, u, v int64 = MOD, 1, 0
	for b > 0 {
		t := a / b
		a -= t * b
		a, b = b, a
		u -= t * v
		u, v = v, u
	}
	u %= MOD
	if u < 0 {
		u += MOD
	}
	return u
}

type Q struct {
	value int
	index int
	K     int
}

type QS []*Q

func (p QS) Len() int           { return len(p) }
func (p QS) Less(i, j int) bool { return p[i].value > p[j].value }
func (pq QS) Swap(i, j int) {
	pq[i], pq[j] = pq[j], pq[i]
	pq[i].index = i
	pq[j].index = j
}

func (pq *QS) Push(x interface{}) {
	n := len(*pq)
	item := x.(*Q)
	item.index = n
	*pq = append(*pq, item)
}

func (pq *QS) Pop() interface{} {
	old := *pq
	n := len(old)
	item := old[n-1]
	old[n-1] = nil  // avoid memory leak
	item.index = -1 // for safety
	*pq = old[0 : n-1]
	return item
}

func GCD(a, b int64) int64 {
	if b == 0 {
		return a
	}
	return GCD(b, a%b)
}

func LCM(a, b int64) int64 {
	return a * b / GCD(a, b)
}

type UnionFind struct {
	par  []int
	size []int
}

func NewUnionFind(size int) *UnionFind {
	return new(UnionFind).init(size)
}

func (uf *UnionFind) init(size int) *UnionFind {
	uf.par = make([]int, size)
	uf.size = make([]int, size)

	for i := 0; i < size; i++ {
		uf.par[i] = i
		uf.size[i] = 1
	}
	return uf
}

func (uf *UnionFind) Unite(p int, q int) {
	rp := uf.Root(p)
	rq := uf.Root(q)
	if rp == rq {
		return
	}
	if uf.size[rp] < uf.size[rq] {
		uf.par[rp] = uf.par[rq]
		uf.size[rq] += uf.size[rp]
	} else {
		uf.par[rq] = uf.par[rp]
		uf.size[rp] += uf.size[rq]
	}
}

func (uf *UnionFind) Root(p int) int {
	for uf.par[p] == p {
		return p
	}
	uf.par[p] = uf.Root(uf.par[p])
	return uf.par[p]
}

func (uf *UnionFind) Size(p int) int {
	return uf.size[uf.Root(p)]
}

func (uf *UnionFind) Same(p int, q int) bool {
	return uf.Root(p) == uf.Root(q)
}

var sc = bufio.NewScanner(os.Stdin)

func getInt() int {
	n, _ := strconv.Atoi(getStr())
	return n
}

func getStr() string {
	sc.Scan()
	return sc.Text()
}

func factor(result map[int]int, num, pnum int) map[int]int {
	if pnum*pnum > num {
		if num != 1 {
			result[num] += 1
		}
		return result
	}

	if num%pnum == 0 {
		num /= pnum
		result[pnum]++
	} else {
		pnum++
	}
	return factor(result, num, pnum)
}

func main() {
	R := []rune(getStr())
	var rxs []rune
	for _, r := range R {
		s := string(r)
		if s == "x" {
			continue
		}
		rxs = append(rxs, r)
	}
	piv := len(rxs) / 2
	l := piv - 1
	r := piv + 1
	if len(rxs)%2 == 0 {
		r--
	}
	var lr, rr []rune
	for i := 0; i <= l; i++ {
		lr = append(lr, rxs[i])
	}
	for i := len(rxs) - 1; i >= r; i-- {
		rr = append(rr, rxs[i])
	}
	if string(lr) != string(rr) {
		fmt.Println(-1)
		return
	}

	var ans int
	start := 0
	end := len(R) - 1
	for start < end {
		s := string(R[start])
		es := string(R[end])
		if s == "x" {
			l++
		}
		if s == es {
			start++
			end--
		} else if s == "x" {
			ans++
			start++
		} else {
			ans++
			end--
		}
	}
	fmt.Println(ans)
}

type IntHeap []int

func (h IntHeap) Len() int           { return len(h) }
func (h IntHeap) Less(i, j int) bool { return h[i] > h[j] }
func (h IntHeap) Swap(i, j int)      { h[i], h[j] = h[j], h[i] }

func (h *IntHeap) Push(x interface{}) {
	// Push and Pop use pointer receivers because they modify the slice's length,
	// not just its contents.
	*h = append(*h, x.(int))
}

func (h *IntHeap) Pop() interface{} {
	old := *h
	n := len(old)
	x := old[n-1]
	*h = old[0 : n-1]
	return x
}

func Reverse(s string) string {
	runes := []rune(s)
	for i, j := 0, len(runes)-1; i < j; i, j = i+1, j-1 {
		runes[i], runes[j] = runes[j], runes[i]
	}
	return string(runes)
}