#include <bits/stdc++.h>
using namespace std;
template <typename T>
struct PrefixSum
{
vector<T> t;
PrefixSum() {}
PrefixSum(vector<T> const &v)
{
t = vector<T>(v.begin(), v.end());
for (size_t i = 1; i < t.size(); i++)
t[i] += t[i - 1];
}
T range_sum(size_t i, size_t j)
{
return t[j] - (i ? t[i - 1] : 0);
}
};
vector<PrefixSum<unsigned>> group_sum;
unsigned sum_groups(size_t i, size_t j, unsigned mask)
{
unsigned x = 0;
for (unsigned k = 0; k < group_sum.size(); k++)
if (mask & (1 << k))
x += group_sum[k].range_sum(i, j);
return x;
}
vector<vector<vector<unsigned>>> num_smaller_members, num_greater_members;
uint64_t sum_smaller_members(unsigned curr_group, unsigned k, unsigned mask)
{
if (k == num_greater_members[curr_group][0].size())
return 0;
uint64_t x = 0;
for (unsigned j = 0; j < num_smaller_members.size(); j++)
if (mask & (1 << j))
x += num_smaller_members[curr_group][j][k];
return x;
}
uint64_t sum_greater_members(unsigned curr_group, unsigned k, unsigned mask)
{
if (k == num_greater_members[curr_group][0].size())
return 0;
uint64_t x = 0;
for (unsigned j = 0; j < num_greater_members.size(); j++)
if (mask & (1 << j))
x += num_greater_members[curr_group][j][k];
return x;
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
string s;
cin >> s;
size_t n = s.size(), g = 1;
for (char const &c : s)
g = max<size_t>(g, c - 'A' + 1);
vector<vector<unsigned>> groups(g);
for (unsigned i = 0; i < n; i++)
groups[s[i] - 'A'].push_back(i);
group_sum = vector<PrefixSum<unsigned>>(g);
for (unsigned i = 0; i < g; i++)
{
vector<unsigned> z(s.size(), 0);
for (unsigned const &j : groups[i])
z[j] = 1;
group_sum[i] = PrefixSum(z);
}
// For each member of a group, the prefix / suffix sum of the number of
// smaller / greater elements of the groups members
num_smaller_members = vector<vector<vector<unsigned>>>(g, vector<vector<unsigned>>(g)),
num_greater_members = vector<vector<vector<unsigned>>>(g, vector<vector<unsigned>>(g));
for (size_t i = 0; i < g; i++)
{
for (size_t j = 0; j < g; j++)
{
num_smaller_members[i][j] = vector<unsigned>(groups[i].size());
for (size_t k = 0; k < groups[i].size(); k++)
num_smaller_members[i][j][k] = group_sum[j].range_sum(0, groups[i][k]);
num_greater_members[i][j] = vector<unsigned>(groups[i].size());
for (size_t k = 0; k < groups[i].size(); k++)
num_greater_members[i][j][k] = group_sum[j].range_sum(groups[i][k], n - 1);
for (size_t k = 1; k < groups[i].size(); k++)
num_smaller_members[i][j][k] += num_smaller_members[i][j][k - 1];
for (size_t k = groups[i].size() - 2; k < groups[i].size(); k--)
num_greater_members[i][j][k] += num_greater_members[i][j][k + 1];
}
}
vector<uint64_t> dp(1 << g, UINT64_MAX);
dp[0] = 0;
for (unsigned mask = 0; mask < 1U << g; mask++)
{
for (unsigned i = 0; i < g; i++)
if (mask & (1 << i)) // Let i be the last group borded.
{
// Binary search over the members of i for the point where it
// is better to board from the back than from the front.
size_t a = 0, b = groups[i].size();
while (a < b)
{
size_t mid = (a + b) / 2;
unsigned front_cost =
sum_groups(0, groups[i][mid], mask ^ (1 << i)) * 2 +
sum_groups(0, groups[i][mid], 1 << i) - 1;
unsigned back_cost =
sum_groups(groups[i][mid], n - 1, mask ^ (1 << i)) * 2 +
sum_groups(groups[i][mid], n - 1, 1 << i) - 1;
if (front_cost < back_cost)
a = mid + 1;
else
b = mid;
}
// a is the first to board backwards.
dp[mask] = min<uint64_t>(dp[mask], dp[mask ^ (1 << i)] +
((a ? sum_smaller_members(i, a - 1, mask ^ (1 << i)) : 0) +
sum_greater_members(i, a, mask ^ (1 << i))) *
2 +
((a > 1) ? sum_smaller_members(i, a - 2, 1 << i) : 0) +
((a + 1 < groups[i].size()) ? sum_greater_members(i, a + 1, 1 << i) : 0));
}
}
cout << setprecision(7) << fixed << (long double)dp.back() / 2.0 << '\n';
}
