#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
using namespace std;
typedef long long int ll;
typedef vector<ll> vi;
typedef vector<vector<ll>> vvi;
typedef pair<ll,ll> pi;
typedef map<ll,ll> mi;
typedef long double ld;
typedef vector<ld> vd;
typedef vector<vector<ld>> vvd;
typedef pair<ld,ld> pd;
#define ff first
#define ss second
#define srt(a) sort(a.begin(),a.end());
#define fip(k, n) for (ll i = k; i < n; i++)
#define fjp(k, n) for (ll j = k; j < n; j++)
#define fin(k, n) for (ll i = k; i >= n; i--)
#define fjn(k, n) for (ll j = k; j >= n; j--)
#define fp(k, n, m) for (ll k = n; k < m; k++)
#define fn(k, n, m) for (ll k = n; k >= m; k--)
#define ordered_set tree<pi, null_type,less< pi >, rb_tree_tag,tree_order_statistics_node_update>
#define totalOne(n) __builtin_popcount(n)
#define backZero(n) __builtin_ctzll(n)
#define frontZero(n) __builtin_clzll(n)
#define fx(k) for ( auto x : k )
#define test ll t;cin >> t;while (t--)
#define nli "\n"
// ==========================(debug)============================================================================================== //
#ifdef SAMI
#define debug(x) cerr<<#x;cerr<<" ";_printn(x);cerr<<nli;
#define debg() cerr<<nli;
#else
#define debug(x)
#define debg()
#endif
void _printn(ll x){ cerr<<x<<" "; }
void _printn(int x){ cerr<<x<<" "; }
void _printn(ld x){ cerr<<x<<" "; }
void _printn(double x){ cerr<<x<<" "; }
void _printn(string x){ cerr<<x<<" "; }
void _printn(char x){ cerr<<x<<" "; }
void _printn(bool x){ cerr<<x<<" "; }
template<class T,class V>void _printn(pair<T,V> vv);
template<class T> void _printn(vector<T> vv);
template<class T> void _printn(set<T> vv);
template<class T,class V> void _printn(map<T,V> vv);
template<class T> void _printn(multiset<T> vv);
template<class T,class V>void _printn(pair<T,V> vv){ cerr<<"( ";_printn(vv.ff);cerr<<",";_printn(vv.ss);cerr<<")";}
template<class T> void _printn(vector<T> vv){ cerr<<"[ "; for(auto xx:vv){ _printn(xx);cerr<<" "; } cerr<<"]"; };
template<class T> void _printn(set<T> vv){ cerr<<"{ "; for(auto xx:vv){ _printn(xx);cerr<<" "; } cerr<<"}"; };
template<class T> void _printn(multiset<T> vv){ cerr<<"{ "; for(auto xx:vv){ _printn(xx);cerr<<" "; } cerr<<"}"; };
template<class T,class V> void _printn(map<T,V> vv){ cerr<<"{ "; for(auto xx:vv){ _printn(xx);cerr<<" "; } cerr<<"}"; };
// ==========================(debug)============================================================================================== //
ll n,m,tp,tp2,res,cnt,sum,tptp,ans;
const ll mx = 1e5+5;
const ll mod = 1e9+7;
// ==========================(MOD)=============================================================================================== //
ll mod_add(ll aa,ll bb){ return ((aa%mod)+(bb%mod))%mod; }
ll mod_minus(ll aa,ll bb){ return (((aa%mod)-(bb%mod))+10*mod)%mod; }
ll mod_mul(ll aa,ll bb){ return ((aa%mod)*(bb%mod))%mod; }
ll mod_power(ll aa,ll bb){ aa%=mod; ll empowered = 1; bb%=mod-1; while(bb > 0){ if(bb & 1) empowered = mod_mul(empowered,aa); bb = bb >> 1; aa = mod_mul(aa,aa); } return empowered; }
ll mod_divi(ll aa,ll bb){ aa=mod_mul(aa,mod_power(bb,mod-2)); return aa; }
// ==========================(MOD)=============================================================================================== //
bool f = false;
string s;
bool mark[mx];
vi lis[mx];
ld dp[1<<16];
ll to[100];
ll from[100];
ll pref[20][mx];
ll suf[20][mx];
ll c[20];
ld get(ld aa,ld bb){
ld rss = aa * (aa-1);
rss += bb * (bb-1);
return (rss/4.0);
}
ld calc(ll id,ll x,ll bt){
ld pt = 0;
fjp(0,tp){
if(bt & (1<<j))
pt += pref[j][lis[x][id]];
}
fjp(0,tp){
if(bt & (1<<j))
pt += suf[j][lis[x][id+1]];
}
pt += get(id+1,cnt-id-1);
return pt;
}
int main(){
ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
#ifdef SAMI
freopen("input1.txt", "r", stdin);
freopen("output1.txt", "w", stdout);
freopen("error1.txt", "w", stderr);
#endif // ONLINE_JUDGE
cin>>s;
// fip(0,899)
// cout<<'A';
n = s.size();
set<char> st;
fx(s)
st.insert(x);
tp = st.size();
fip(0,(1<<tp))
dp[i] = 1e18;
cnt = 0;
fx(st){
to[cnt] = x-'A';
from[x-'A'] = cnt;
cnt++;
}
cnt = 0;
fjp(0,tp){
cnt = 0;
fip(0,tp)
c[i] = 0;
fip(0,n){
tp2 = s[i]-'A';
if(from[tp2]==j)
cnt++;
else{
c[from[tp2]] += cnt;
pref[j][i] = c[from[tp2]];
}
// if(j==2){
// debug(cnt);
// debug(c[from[tp2]]);
// }
}
}
cnt = 0;
fjp(0,tp){
cnt = 0;
fip(0,tp)
c[i] = 0;
fin(n-1,0){
tp2 = s[i]-'A';
if(from[tp2]==j)
cnt++;
else{
c[from[tp2]] += cnt;
suf[j][i] = c[from[tp2]];
}
}
}
// fip(0,n)
// cout<<suf[2][i]<<" ";
// cout<<nli;
ll l,r,mid1,mid2;
ld g1,g2;
dp[0] = 0;
cnt = 0;
fip(0,n)
lis[s[i]-'A'].push_back(i);
cnt = 0;
fip(1,1<<tp){
// v = {1,4,3,6,5};
fjp(0,tp){
if(i & (1<<j))
mark[to[j]] = 1;
else
mark[to[j]] = 0;
}
fjp(0,tp){
ld rs = 0;
ld sm = 0;
if(i & (1<<j)){
tp2 = i-(1<<j);
ll x = to[j];
mark[x] = 0;
cnt = lis[x].size();
sm = 0;
if(i==23){ debug(j);}
fp(k,0,tp){
if(tp2 & (1<<k)){
sm += suf[k][lis[x][0]];
}
}
rs = sm + get(0,cnt);
sm = 0;
fp(k,0,tp){
if(tp2 & (1<<k)){
sm += pref[k][lis[x][lis[x].size()-1]];
}
}
rs = min(rs,sm + get(0,cnt));
debug((ll)lis[x].size())
if(lis[x].size()> 1){
l = 0;
r = lis[x].size() - 2;
while(r-l>=3){
mid1 = l + (r-l) / 3;
mid2 = r - (r-l) / 3;
g1 = calc(mid1,x,tp2);
g2 = calc(mid2,x,tp2);
if(g1 > g2)
l = mid1;
else
r = mid2;
}
fp(tt,l,r+1) {
rs = min(rs,calc(tt,x,tp2));
}
}
mark[x] = 1;
// if(i==7 && dp[i] > dp[tp2]+rs){
// debg();
// debug(l);
// debug(r);
// debug(tp2);
// debug(dp[tp2]+rs);
// cerr<<bitset<3>(tp2)<<nli;
// }
dp[i] = min(dp[i],dp[tp2]+rs);
}
}
// debug(i) ;
// cerr<<bitset<3>(i)<<nli;
// debug(dp[i]);
}
tp = (1ll<<tp) - 1;
cout<<setprecision(20)<<dp[tp]<<nli;
cerr << "Time elapsed: " << setprecision(6) << 1000.0 * clock() / CLOCKS_PER_SEC << "ms\n";
return 0;
}
