This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int N = 100100;
const int K = 15;
ll p[N][K];
ll dp[1 << K];
void solve() {
string s;
cin >> s;
int n = s.size();
vector<int> v(n);
for (int i = 0; i < n; ++i) v[i] = s[i] - 'A';
memset(dp, 0x3f, sizeof dp);
dp[0] = 0;
for (int j = 1; j < (1 << K); ++j) {
for (int i = 0; i < K; ++i) if (j >> i & 1) {
ll l[2]{}, r[2]{}, t = 0;
for (int k : v) {
r[0] += k == i;
if (i != k && (j >> k & 1)) {
++r[1];
t += r[0];
}
}
dp[j] = min(dp[j], dp[j ^ (1 << i)] + r[0]*(r[0]-1)/2 + 2*t);
for (int k : v) {
l[0] += k == i;
r[0] -= k == i;
l[1] += i != k && (j >> k & 1);
r[1] -= i != k && (j >> k & 1);
if (k == i) {
t -= r[1];
t += l[1];
}
dp[j] = min(dp[j], dp[j ^ (1 << i)] + l[0]*(l[0]-1)/2 + r[0]*(r[0]-1)/2 + 2*t);
}
//cout << bitset<3>(j) << ' ' << bitset<3>(1 << i) << ": " << dp[j] << '\n';
}
}
cout << (long double) dp[(1 << K) - 1] / 2.0 << '\n';
}
int main() {
cin.tie(0) -> sync_with_stdio(0);
cout << fixed << setprecision(6);
solve();
}
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