Problem:
Score : 800 points

Problem Statement

You are given a string S consisting of lowercase English letters.
Determine whether we can turn S into a palindrome by repeating the operation of swapping two adjacent characters. If it is possible, find the minimum required number of operations.

Constraints

1 \leq |S| \leq 2 × 10^5

S consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

S

Output

If we cannot turn S into a palindrome, print -1. Otherwise, print the minimum required number of operations.

Sample Input 1

eel

Sample Output 1

1

We can turn S into a palindrome by the following operation:

Swap the 2-nd and 3-rd characters. S is now ele.

Sample Input 2

ataatmma

Sample Output 2

4

We can turn S into a palindrome by the following operation:

Swap the 5-th and 6-th characters. S is now ataamtma.

Swap the 4-th and 5-th characters. S is now atamatma.

Swap the 3-rd and 4-th characters. S is now atmaatma.

Swap the 2-nd and 3-rd characters. S is now amtaatma.

Sample Input 3

snuke

Sample Output 3

-1

We cannot turn S into a palindrome.

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

//Zory-2020
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
// typedef __int128 ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define FR first
#define SE second
#define MP make_pair
#define PB push_back
#define vc vector
#define db double
#define all(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define bin(x) (1ll<<(x))
#define fo(i,l,r) for(int i=(l),I=(r);i<=I;i++)
#define fd(i,r,l) for(int i=(r),I=(l);i>=I;i--)
#define mem(x,val) memset(x,val,sizeof x)
#define Swap(a,b,n) for(int I=0;I<=n;I++) swap(a[I],b[I])
#define PC __builtin_popcountll
#ifdef DEBUG
	#define debug(A,args...) fprintf(stderr,A,##args)
#else
	#define debug(A,args...) printf("")
#endif
#define deb debug("line %d\n",__LINE__)
namespace mine
{
	ll qread()
	{
		ll ans=0,f=1;char c=getchar();
		while(c<'0' or c>'9') {if(c=='-')f=-1;c=getchar();}
		while('0'<=c and c<='9') ans=ans*10+c-'0',c=getchar();
		return ans*f;
	}
	void write(ll num){if(num<0) putchar('-'),num=-num;if(num>=10) write(num/10);putchar('0'+num%10);}
	void write1(ll num){write(num);putchar(' ');}
	void write2(ll num){write(num);putchar('\n');}
	template<typename T>inline bool chmax(T&a,const T&b){return a<b?a=b,1:0;}
	template<typename T>inline bool chmin(T&a,const T&b){return a>b?a=b,1:0;}
	ll gcd(ll x,ll y){return y?gcd(y,x%y):x;}
	bool IN(ll x,ll l,ll r){return l<=x and x<=r;}
	void GG(){puts("-1");exit(0);}
	
	const db eps=1e-8;
	const int INF=0x3f3f3f3f;
	const int MOD=1e9+7;
	int mm(const int x){return x>=MOD?x-MOD:x;}
	template<typename T> void add(T &x,const int &y){x=(x+y>=MOD?x+y-MOD:x+y);}
	ll qpower(ll x,ll e,int mod=MOD){ll ans=1;while(e){if(e&1)ans=ans*x%mod;x=x*x%mod;e>>=1;}return ans;}
	ll invm(ll x){return qpower(x,MOD-2);}
	const int M=1e3+10;
	ll fac[M],facinv[M],Inv[M];ll C(int n,int m){return n<0 or n<m?0:fac[n]*facinv[m]%MOD*facinv[n-m]%MOD;}
	void PRE()
	{
		fac[0]=1;fo(i,1,M-1) fac[i]=fac[i-1]*i%MOD;
		facinv[M-1]=invm(fac[M-1]);fd(i,M-1,1) facinv[i-1]=facinv[i]*i%MOD;
		Inv[1]=1;fo(i,2,M-1) Inv[i]=(MOD-MOD/i)*Inv[MOD%i]%MOD;
	}
	const int N=1e6+10;
	//------------------FIXED------------------
	//��״����
	struct BIT
	{
		int bit[N];int lowbit(int x){return x&-x;}
		void ad(int x,int c){ while(x<N) bit[x]+=c,x+=lowbit(x); }
		int ask(int x){ int ret=0;while(x>=1) ret+=bit[x],x-=lowbit(x);return ret; }
	}bit;
	char str[N];deque<int> pos[30];bool ok[N];
	void main()
	{
		scanf("%s",str+1);int n=strlen(str+1);fo(i,1,n) pos[str[i]-'a'].PB(i);
		fo(i,1,n) bit.ad(i,1);int ct=0;fo(i,0,25)ct+=sz(pos[i])%2;if(ct>n%2) GG();
		ll ans=0;
		fo(i,1,n) if(!ok[i])
		{
			int col=str[i]-'a',j=pos[col].back();ok[i]=ok[j]=1;
			pos[col].pop_front(),bit.ad(i,-1);
			if(i!=j) pos[col].pop_back(),bit.ad(j,-1),ans+=bit.ask(n)-bit.ask(j);
			else if(i<(n+1)/2) ans+=bit.ask((n+1)/2)-bit.ask(i);
			else ans+=bit.ask(i)-bit.ask((n+1)/2-1);
		}write(ans);
	}
};//����������
signed main()
{
	#ifdef DEBUG
	//freopen("a.in","r",stdin);
	freopen("z.txt","r",stdin);
	//freopen("a.out","w",stdout);
	#endif
	srand(time(0));
	mine::PRE();//����Ԥ����ģ����
	mine::main();
	debug("\n---------------------Zory---------------------\nTime: %.2lf s",1.0*clock()/CLOCKS_PER_SEC);
}