This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
/*
* File created on 07/19/2022 at 15:24:35.
* Link to problem:
* Description:
* Time complexity: O()
* Space complexity: O()
* Status: ---
* Copyright: Ⓒ 2022 Francois Vogel
*/
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
#define pii pair<int, int>
#define f first
#define s second
#define vi vector<int>
#define all(x) x.begin(), x.end()
#define size(x) (int)((x).size())
#define pb push_back
#define ins insert
#define cls clear
#define int ll
#define ll long long
#define ld long double
typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
signed main() {
cin.tie(0);
ios_base::sync_with_stdio(0);
string b;
cin >> b;
const int n = size(b);
int gK = 0;
for (char i : b) if (i-'A'+1 > gK) gK = i-'A'+1;
vi toPermute;
for (int i = 0; i < gK; i++) toPermute.pb(i);
ld offMin = n*n;
do {
for (int i = 0; i < n; i++) {
b[i] = char('A'+toPermute[b[i]-'A']);
}
ld res = 0;
for (int i = 0; i < gK; i++) {
vi pos;
for (int j = 0; j < n; j++) if (b[j]-'A' == i) {
pos.pb(j);
}
if (pos.empty()) continue;
int pref [n];
for (int j = 0; j < n; j++) pref[j] = (b[j]-'A' < i);
for (int j = 1; j < n; j++) pref[j] += pref[j-1];
int suf [n];
for (int j = 0; j < n; j++) suf[j] = (b[j]-'A' < i);
for (int j = n-2; j >= 0; j--) suf[j] += suf[j+1];
for (int j = 0; j < size(pos); j++) {
ld dl = 0;
if (pos[j]) dl = pref[pos[j]-1];
ld dr = 0;
if (pos[j]+1 < n) dr = suf[pos[j]+1];
ld cl = j;
ld cr = size(pos)-1-j;
res += min(dl+cl/2, dr+cr/2);
}
}
offMin = min(offMin, res);
vi invToPermute(gK);
for (int i = 0; i < gK; i++) invToPermute[toPermute[i]] = i;
for (int i = 0; i < n; i++) {
b[i] = char('A'+invToPermute[b[i]-'A']);
}
} while (next_permutation(all(toPermute)));
cout.precision(20);
cout << offMin;
cout.flush();
int d = 0;
d++;
}
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