#line 1 "main.cpp"
/**
* @title Template
*/
#include <iostream>
#include <algorithm>
#include <utility>
#include <numeric>
#include <vector>
#include <array>
#include <cassert>
#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/other/chmin_chmax.cpp"
template <class T, class U>
constexpr bool chmin(T &lhs, const U &rhs) {
if (lhs > rhs) { lhs = rhs; return true; }
return false;
}
template <class T, class U>
constexpr bool chmax(T &lhs, const U &rhs) {
if (lhs < rhs) { lhs = rhs; return true; }
return false;
}
/**
* @title Chmin/Chmax
*/
#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/other/range.cpp"
#line 4 "/Users/kodamankod/Desktop/cpp_programming/Library/other/range.cpp"
class range {
public:
class iterator {
private:
int64_t M_position;
public:
constexpr iterator(int64_t position) noexcept: M_position(position) { }
constexpr void operator ++ () noexcept { ++M_position; }
constexpr bool operator != (iterator other) const noexcept { return M_position != other.M_position; }
constexpr int64_t operator * () const noexcept { return M_position; }
};
class reverse_iterator {
private:
int64_t M_position;
public:
constexpr reverse_iterator(int64_t position) noexcept: M_position(position) { }
constexpr void operator ++ () noexcept { --M_position; }
constexpr bool operator != (reverse_iterator other) const noexcept { return M_position != other.M_position; }
constexpr int64_t operator * () const noexcept { return M_position; }
};
private:
const iterator M_first, M_last;
public:
constexpr range(int64_t first, int64_t last) noexcept: M_first(first), M_last(std::max(first, last)) { }
constexpr iterator begin() const noexcept { return M_first; }
constexpr iterator end() const noexcept { return M_last; }
constexpr reverse_iterator rbegin() const noexcept { return reverse_iterator(*M_last - 1); }
constexpr reverse_iterator rend() const noexcept { return reverse_iterator(*M_first - 1); }
};
/**
* @title Range
*/
#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/other/rev.cpp"
#include <type_traits>
#include <iterator>
#line 6 "/Users/kodamankod/Desktop/cpp_programming/Library/other/rev.cpp"
template <class T>
class rev_impl {
public:
using iterator = decltype(std::rbegin(std::declval<T>()));
private:
const iterator M_begin;
const iterator M_end;
public:
constexpr rev_impl(T &&cont) noexcept: M_begin(std::rbegin(cont)), M_end(std::rend(cont)) { }
constexpr iterator begin() const noexcept { return M_begin; }
constexpr iterator end() const noexcept { return M_end; }
};
template <class T>
constexpr decltype(auto) rev(T &&cont) {
return rev_impl<T>(std::forward<T>(cont));
}
/**
* @title Reverser
*/
#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/container/fenwick_tree.cpp"
#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/other/bit_operation.cpp"
#include <cstddef>
#include <cstdint>
constexpr size_t bit_ppc(const uint64_t x) { return __builtin_popcountll(x); }
constexpr size_t bit_ctzr(const uint64_t x) { return x == 0 ? 64 : __builtin_ctzll(x); }
constexpr size_t bit_ctzl(const uint64_t x) { return x == 0 ? 64 : __builtin_clzll(x); }
constexpr size_t bit_width(const uint64_t x) { return 64 - bit_ctzl(x); }
constexpr uint64_t bit_msb(const uint64_t x) { return x == 0 ? 0 : uint64_t(1) << (bit_width(x) - 1); }
constexpr uint64_t bit_lsb(const uint64_t x) { return x & (-x); }
constexpr uint64_t bit_cover(const uint64_t x) { return x == 0 ? 0 : bit_msb(2 * x - 1); }
constexpr uint64_t bit_rev(uint64_t x) {
x = ((x >> 1) & 0x5555555555555555) | ((x & 0x5555555555555555) << 1);
x = ((x >> 2) & 0x3333333333333333) | ((x & 0x3333333333333333) << 2);
x = ((x >> 4) & 0x0F0F0F0F0F0F0F0F) | ((x & 0x0F0F0F0F0F0F0F0F) << 4);
x = ((x >> 8) & 0x00FF00FF00FF00FF) | ((x & 0x00FF00FF00FF00FF) << 8);
x = ((x >> 16) & 0x0000FFFF0000FFFF) | ((x & 0x0000FFFF0000FFFF) << 16);
x = (x >> 32) | (x << 32);
return x;
}
/**
* @title Bit Operations
*/
#line 4 "/Users/kodamankod/Desktop/cpp_programming/Library/container/fenwick_tree.cpp"
#line 8 "/Users/kodamankod/Desktop/cpp_programming/Library/container/fenwick_tree.cpp"
#include <type_traits>
template <class T>
class fenwick_tree {
public:
using value_type = T;
using size_type = size_t;
private:
std::vector<value_type> M_tree;
public:
fenwick_tree() = default;
explicit fenwick_tree(size_type size) { initialize(size); }
void initialize(size_type size) {
M_tree.assign(size + 1, value_type { });
}
void add(size_type index, const value_type& x) {
assert(index < size());
++index;
while (index <= size()) {
M_tree[index] += x;
index += bit_lsb(index);
}
}
template <size_type Indexed = 1>
value_type get(size_type index) const {
assert(index < size());
index += Indexed;
value_type res{ };
while (index > 0) {
res += M_tree[index];
index -= bit_lsb(index);
}
return res;
}
value_type fold(size_type first, size_type last) const {
assert(first <= last);
assert(last <= size());
value_type res{};
while (first < last) {
res += M_tree[last];
last -= bit_lsb(last);
}
while (last < first) {
res -= M_tree[first];
first -= bit_lsb(first);
}
return res;
}
template <class Func>
size_type satisfies(const size_type left, Func &&func) const {
assert(left <= size());
if (func(value_type { })) return left;
value_type val = -get<0>(left);
size_type res = 0;
for (size_type cur = bit_cover(size() + 1) >> 1; cur > 0; cur >>= 1) {
if ((res + cur <= left) || (res + cur <= size() && !func(val + M_tree[res + cur]))) {
val += M_tree[res + cur];
res += cur;
}
}
return res + 1;
}
void clear() {
M_tree.clear();
M_tree.shrink_to_fit();
}
size_type size() const {
return M_tree.size() - 1;
}
};
/**
* @title Fenwick Tree
*/
#line 18 "main.cpp"
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
constexpr i32 inf32 = (i32(1) << 30) - 1;
constexpr i64 inf64 = (i64(1) << 62) - 1;
int main() {
std::ios_base::sync_with_stdio(false);
std::cin.tie(nullptr);
size_t N;
std::cin >> N;
std::vector<bool> color(2 * N);
for (auto i: range(0, 2 * N)) {
char c;
std::cin >> c;
color[i] = (c == 'B');
}
if (color[0]) {
for (auto i: range(0, 2 * N)) {
color[i] = !color[i];
}
}
std::vector<i32> W, B;
W.reserve(N);
B.reserve(N);
for (auto i: range(0, 2 * N)) {
(color[i] ? B : W).push_back(i);
}
const auto solve = [&](const size_t K) {
std::vector<i32> partner(2 * N);
for (auto i: range(0, N)) {
const auto j = (i + K) % N;
partner[W[i]] = B[j];
partner[B[j]] = W[i];
}
fenwick_tree<i32> fen(2 * N);
i64 sum = 0;
for (auto i: range(0, 2 * N)) {
if (partner[i] > i) {
sum += fen.fold(i + 1, partner[i]);
fen.add(partner[i], 1);
}
}
return sum;
};
i64 ans = 0;
i32 l = 0, r = N - 1;
while (r - l > 2) {
const auto m1 = (l + r) / 2;
const auto m2 = m1 + 1;
const auto v1 = solve(m1);
const auto v2 = solve(m2);
if (v1 < v2) {
l = m1;
}
else {
r = m2;
}
}
for (auto k: range(l, r + 1)) {
chmax(ans, solve(k));
}
std::cout << ans << '\n';
return 0;
}
