結果
| 問題 | No.1504 ヌメロニム |
| ユーザー |
 minato
|
| 提出日時 | 2023-07-20 05:01:59 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 171 ms / 2,000 ms |
| コード長 | 27,612 bytes |
| コンパイル時間 | 1,897 ms |
| コンパイル使用メモリ | 155,028 KB |
| 実行使用メモリ | 30,772 KB |
| 最終ジャッジ日時 | 2024-09-20 02:09:29 |
| 合計ジャッジ時間 | 7,669 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 16 ms
11,008 KB |
| testcase_01 | AC | 15 ms
11,008 KB |
| testcase_02 | AC | 15 ms
10,896 KB |
| testcase_03 | AC | 15 ms
11,008 KB |
| testcase_04 | AC | 16 ms
11,008 KB |
| testcase_05 | AC | 15 ms
10,864 KB |
| testcase_06 | AC | 15 ms
10,996 KB |
| testcase_07 | AC | 15 ms
11,008 KB |
| testcase_08 | AC | 15 ms
11,008 KB |
| testcase_09 | AC | 15 ms
10,996 KB |
| testcase_10 | AC | 15 ms
11,008 KB |
| testcase_11 | AC | 15 ms
11,008 KB |
| testcase_12 | AC | 15 ms
10,880 KB |
| testcase_13 | AC | 15 ms
11,008 KB |
| testcase_14 | AC | 15 ms
10,984 KB |
| testcase_15 | AC | 15 ms
10,892 KB |
| testcase_16 | AC | 15 ms
11,064 KB |
| testcase_17 | AC | 16 ms
10,880 KB |
| testcase_18 | AC | 15 ms
11,008 KB |
| testcase_19 | AC | 15 ms
10,988 KB |
| testcase_20 | AC | 16 ms
11,060 KB |
| testcase_21 | AC | 16 ms
11,116 KB |
| testcase_22 | AC | 16 ms
11,136 KB |
| testcase_23 | AC | 16 ms
11,008 KB |
| testcase_24 | AC | 163 ms
29,932 KB |
| testcase_25 | AC | 91 ms
22,284 KB |
| testcase_26 | AC | 162 ms
30,564 KB |
| testcase_27 | AC | 92 ms
23,304 KB |
| testcase_28 | AC | 93 ms
23,452 KB |
| testcase_29 | AC | 163 ms
30,404 KB |
| testcase_30 | AC | 158 ms
30,404 KB |
| testcase_31 | AC | 92 ms
22,696 KB |
| testcase_32 | AC | 94 ms
23,268 KB |
| testcase_33 | AC | 163 ms
30,256 KB |
| testcase_34 | AC | 34 ms
13,976 KB |
| testcase_35 | AC | 33 ms
13,684 KB |
| testcase_36 | AC | 90 ms
20,652 KB |
| testcase_37 | AC | 24 ms
12,364 KB |
| testcase_38 | AC | 161 ms
30,632 KB |
| testcase_39 | AC | 163 ms
30,608 KB |
| testcase_40 | AC | 162 ms
30,772 KB |
| testcase_41 | AC | 163 ms
30,632 KB |
| testcase_42 | AC | 171 ms
30,484 KB |
| testcase_43 | AC | 164 ms
30,648 KB |
| testcase_44 | AC | 163 ms
30,608 KB |
| testcase_45 | AC | 165 ms
30,644 KB |
| testcase_46 | AC | 167 ms
30,616 KB |
| testcase_47 | AC | 165 ms
30,644 KB |
| testcase_48 | AC | 92 ms
22,848 KB |
| testcase_49 | AC | 90 ms
22,288 KB |
| testcase_50 | AC | 17 ms
11,136 KB |
| testcase_51 | AC | 16 ms
11,008 KB |
| testcase_52 | AC | 15 ms
10,984 KB |
| testcase_53 | AC | 16 ms
11,096 KB |
| testcase_54 | AC | 15 ms
11,008 KB |
| testcase_55 | AC | 33 ms
13,544 KB |
| testcase_56 | AC | 17 ms
11,008 KB |
| testcase_57 | AC | 16 ms
11,008 KB |
| testcase_58 | AC | 15 ms
11,008 KB |
| testcase_59 | AC | 15 ms
11,008 KB |
| testcase_60 | AC | 15 ms
11,008 KB |
ソースコード
#line 1 "library-cpp/other/template.hpp"
// clang-format off
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
using i128 = __int128_t;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
template <class T> using maxheap = priority_queue<T>;
template <class T> using minheap = priority_queue<T, vector<T>, greater<T>>;
template <class T> using vec = vector<T>;
template <class T> using vvec = vector<vector<T>>;
#define OVERLOAD_REP(_1, _2, _3, name, ...) name
#define REP0(n) for (auto minato = decay_t<decltype(n)>{}; minato < (n); ++minato)
#define REP1(i, n) for (auto i = decay_t<decltype(n)>{}; (i) < (n); (i)++)
#define REP2(i, l, r) for (auto i = (l); (i) < (r); (i)++)
#define rep(...) OVERLOAD_REP(__VA_ARGS__, REP2, REP1, REP0)(__VA_ARGS__)
#define OVERLOAD_RREP(_1, _2, _3, name, ...) name
#define RREP1(i, n) for (auto i = (n) - 1; (i) >= decay_t<decltype(n)>{}; (i)--)
#define RREP2(i, l, r) for (auto i = (r) - 1; (i) >= (l); (i)--)
#define rrep(...) OVERLOAD_RREP(__VA_ARGS__, RREP2, RREP1)(__VA_ARGS__)
#define ALL(x) begin(x), end(x)
template <class Container> int SZ(const Container& v) { return int(v.size()); }
template <class T> void UNIQUE(vector<T>& v) { v.erase(unique(v.begin(), v.end()), v.end()); }
template <class T> T MAX(const vector<T>& v) { return *max_element(v.begin(), v.end()); }
template <class T> T MIN(const vector<T>& v) { return *min_element(v.begin(), v.end()); }
template <class T> T SUM(const vector<T>& v) { return accumulate(v.begin(), v.end(), T(0)); }
template <class T> T ABS(T x) { return max(x, -x); }
template <class T1, class T2> bool chmax(T1& a, T2 b) { if (a < b) { a = b; return true; } return false; }
template <class T1, class T2> bool chmin(T1& a, T2 b) { if (a > b) { a = b; return true; } return false; }
int topbit(ull x) { return x == 0 ? -1 : 63 - __builtin_clzll(x); }
int botbit(ull x) { return x == 0 ? 64 : __builtin_ctzll(x); }
int popcount(ull x) { return __builtin_popcountll(x); }
int kthbit(ull x, int k) { return (x >> k) & 1; }
constexpr long long TEN(int x) { return x == 0 ? 1 : TEN(x - 1) * 10; }
template <typename S> void rearrange(const vector<S>& id) { (void)id; }
template <typename S, typename T> void rearrange_exec(const vector<S>& id, vector<T>& v) { vector<T> w(v.size()); for (size_t i = 0; i < id.size(); i++) { w[i] = v[id[i]]; } v.swap(w); }
template <typename S, typename Head, typename... Tail> void rearrange(const vector<S>& id, Head& a, Tail& ...tail) { rearrange_exec(id, a); rearrange(id, tail...); }
istream& operator>>(istream& is, __int128_t& x) {
x = 0;
string s;
is >> s;
int n = int(s.size()), it = 0;
if (s[0] == '-') it++;
for (; it < n; it++) x = (x * 10 + s[it] - '0');
if (s[0] == '-') x = -x;
return is;
}
ostream& operator<<(ostream& os, __int128_t x) {
if (x == 0) return os << 0;
if (x < 0) os << '-', x = -x;
deque<int> deq;
while (x) deq.emplace_front(x % 10), x /= 10;
for (int e : deq) os << e;
return os;
}
template <class T> vector<T> &operator++(vector<T>& v) { for (auto& e : v) { e++; } return v;}
template <class T> vector<T> operator++(vector<T>& v, int) { auto res = v; for (auto& e : v) { e++; } return res; }
template <class T> vector<T> &operator--(vector<T>& v) { for (auto& e : v) { e--; } return v; }
template <class T> vector<T> operator--(vector<T>& v, int) { auto res = v; for (auto& e : v) { e--; } return res; }
template <class T1, class T2> pair<T1, T2> operator-(const pair<T1, T2>& x) { return pair<T1, T2>(-x.first, -x.second); }
template <class T1, class T2> pair<T1, T2> operator-(const pair<T1, T2>& x, const pair<T1, T2>& y) { return pair<T1, T2>(x.first - y.first, x.second - y.second); }
template <class T1, class T2> pair<T1, T2> operator+(const pair<T1, T2>& x, const pair<T1, T2>& y) { return pair<T1, T2>(x.first + y.first, x.second + y.second); }
template <class T1, class T2> pair<T1, T2> operator+=(pair<T1, T2>& l, const pair<T1, T2>& r) { return l = l + r; }
template <class T1, class T2> pair<T1, T2> operator-=(pair<T1, T2>& l, const pair<T1, T2>& r) { return l = l - r; }
constexpr char ln = '\n';
const string YESNO[2] = {"NO", "YES"};
const string YesNo[2] = {"No", "Yes"};
void YES(bool t = true) { cout << YESNO[t] << "\n"; }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = true) { cout << YesNo[t] << "\n"; }
void No(bool t = 1) { Yes(!t); }
template <class T> void drop(T x) { cout << x << "\n"; exit(0); }
#define INT(...) \
int __VA_ARGS__; \
IN(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
IN(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
IN(__VA_ARGS__)
#define CHR(...) \
char __VA_ARGS__; \
IN(__VA_ARGS__)
#define LDB(...) \
long double __VA_ARGS__; \
IN(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
IN(name)
#define VEC2(type, name1, name2, size) \
vector<type> name1(size), name2(size); \
for (int i = 0; i < size; i++) IN(name1[i], name2[i])
#define VEC3(type, name1, name2, name3, size) \
vector<type> name1(size), name2(size), name3(size); \
for (int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i])
#define VEC4(type, name1, name2, name3, name4, size) \
vector<type> name1(size), name2(size), name3(size), name4(size); \
for (int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i], name4[i]);
#define VV(type, name, N, M) \
vector<vector<type>> name(N, vector<type>(M)); \
IN(name)
template <class T> void scan(T& a) { cin >> a; }
template <class T> void scan(vector<T>& a) { for (auto& i : a) scan(i); }
void IN() {}
template <class Head, class... Tail> void IN(Head& head, Tail&... tail) { scan(head); IN(tail...); }
void print() { cout << "\n"; }
template <class T> void print(const vector<T>& v) { for (auto it = v.begin(); it != v.end(); ++it) { if (it != v.begin()) { cout << " "; } cout << *it; } print(); }
template <class T, class... Args> void print(const T& x, const Args& ... args) { cout << x; if (sizeof...(Args)) cout << " "; print(args...); }
#ifdef MINATO_LOCAL
template <class T1, class T2> ostream& operator<<(ostream& os, pair<T1, T2> p) { return os << "(" << p.first << ", " << p.second << ")"; }
template <size_t N, class TUPLE> void debug_tuple(ostream& os, TUPLE _) { (void)os; (void)_; }
template <size_t N, class TUPLE, class T, class ...Args> void debug_tuple(ostream &os, TUPLE t) { os << (N == 0 ? "" : ", ") << get<N>(t); debug_tuple<N + 1, TUPLE, Args...>(os, t); }
template <class ...Args> ostream& operator<<(ostream& os, tuple<Args...> t) { os << "("; debug_tuple<0, tuple<Args...>, Args...>(os, t); return os << ")"; }
string debug_delim(int& i) { return i++ == 0 ? "" : ", "; }
#define debug_embrace(x) { int i = 0; os << "{"; { x } return os << "}"; }
template <class T> ostream& operator<<(ostream& os, vector<T> v) { debug_embrace( for (T e : v) { os << debug_delim(i) << e; } ) }
template <class T, size_t N> ostream& operator<<(ostream& os, array<T, N> a) { debug_embrace( for (T e : a) { os << debug_delim(i) << e; } ) }
template <class T, size_t N> enable_if_t<!is_same_v<char, remove_cv_t<T>>, ostream>& operator<<(ostream& os, T(&a)[N]) { debug_embrace( for (T e : a) { os << debug_delim(i) << e; } ) }
template <class Key> ostream& operator<<(ostream& os, set<Key> s) { debug_embrace( for (Key e : s) { os << debug_delim(i) << e; }) }
template <class Key, class T> ostream& operator<<(ostream& os, map<Key, T> mp) { debug_embrace( for (auto e : mp) { os << debug_delim(i) << e; }) }
template <class Key> ostream& operator<<(ostream& os, multiset<Key> s) { debug_embrace( for (Key e : s) { os << debug_delim(i) << e; }) }
template <class T> ostream& operator<<(ostream& os, queue<T> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.front(); } ) }
template <class T> ostream& operator<<(ostream& os, deque<T> q) { debug_embrace( for (T e : q) { os << debug_delim(i) << e; } ) }
template <class T> ostream& operator<<(ostream& os, priority_queue<T> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.top(); } ) }
template <class T> ostream& operator<<(ostream& os, priority_queue<T, vector<T>, greater<T>> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.top(); } ) }
void debug_out() { cerr << endl; }
template <class T, class... Args> void debug_out(const T& x, const Args& ... args) { cerr << " " << x; debug_out(args...); }
#define debug(...) cerr << __LINE__ << " : [" << #__VA_ARGS__ << "] =", debug_out(__VA_ARGS__)
#else
#define debug(...) (void(0))
#endif
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// clang-format on
#line 2 "library-cpp/mod/ModInt.hpp"
#line 2 "library-cpp/other/type_traits.hpp"
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
#line 4 "library-cpp/mod/ModInt.hpp"
#line 6 "library-cpp/mod/ModInt.hpp"
template <int m> struct ModInt {
public:
static constexpr int mod() {
return m;
}
static ModInt raw(int v) {
ModInt x;
x._v = v;
return x;
}
ModInt() : _v(0) {
}
template <class T, internal::is_signed_int_t<T>* = nullptr> ModInt(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr> ModInt(T v) {
_v = (unsigned int)(v % umod());
}
unsigned int val() const {
return _v;
}
ModInt& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
ModInt& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
ModInt operator++(int) {
ModInt result = *this;
++*this;
return result;
}
ModInt operator--(int) {
ModInt result = *this;
--*this;
return result;
}
ModInt& operator+=(const ModInt& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
ModInt& operator-=(const ModInt& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
ModInt& operator*=(const ModInt& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
ModInt& operator^=(long long n) {
ModInt x = *this;
*this = 1;
if (n < 0) x = x.inv(), n = -n;
while (n) {
if (n & 1) *this *= x;
x *= x;
n >>= 1;
}
return *this;
}
ModInt& operator/=(const ModInt& rhs) {
return *this = *this * rhs.inv();
}
ModInt operator+() const {
return *this;
}
ModInt operator-() const {
return ModInt() - *this;
}
explicit operator bool() const {
return _v != 0;
}
ModInt pow(long long n) const {
ModInt r = *this;
r ^= n;
return r;
}
ModInt inv() const {
int a = _v, b = umod(), y = 1, z = 0, t;
for (;;) {
t = a / b;
a -= t * b;
if (a == 0) {
assert(b == 1 || b == -1);
return ModInt(b * z);
}
y -= t * z;
t = b / a;
b -= t * a;
if (b == 0) {
assert(a == 1 || a == -1);
return ModInt(a * y);
}
z -= t * y;
}
}
friend ModInt operator+(const ModInt& lhs, const ModInt& rhs) {
return ModInt(lhs) += rhs;
}
friend ModInt operator-(const ModInt& lhs, const ModInt& rhs) {
return ModInt(lhs) -= rhs;
}
friend ModInt operator*(const ModInt& lhs, const ModInt& rhs) {
return ModInt(lhs) *= rhs;
}
friend ModInt operator/(const ModInt& lhs, const ModInt& rhs) {
return ModInt(lhs) /= rhs;
}
friend ModInt operator^(const ModInt& lhs, long long rhs) {
return ModInt(lhs) ^= rhs;
}
friend bool operator==(const ModInt& lhs, const ModInt& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const ModInt& lhs, const ModInt& rhs) {
return lhs._v != rhs._v;
}
friend ModInt operator+(long long lhs, const ModInt& rhs) {
return (ModInt(lhs) += rhs);
}
friend ModInt operator-(long long lhs, const ModInt& rhs) {
return (ModInt(lhs) -= rhs);
}
friend ModInt operator*(long long lhs, const ModInt& rhs) {
return (ModInt(lhs) *= rhs);
}
friend ostream& operator<<(ostream& os, const ModInt& M) {
return os << M._v;
}
friend istream& operator>>(istream& is, ModInt& M) {
long long x;
is >> x;
M = x;
return is;
}
private:
unsigned int _v;
static constexpr unsigned int umod() {
return m;
}
};
#line 2 "library-cpp/mod/ModCombination.hpp"
#line 5 "library-cpp/mod/ModCombination.hpp"
template <class M> struct ModCombination {
public:
ModCombination() {
}
ModCombination(int n) : n_(n), fac_(n + 1), facinv_(n + 1) {
assert(1 <= n);
fac_[0] = 1;
for (int i = 1; i <= n; i++) fac_[i] = fac_[i - 1] * i;
facinv_[n] = M(1) / fac_[n];
for (int i = n; i >= 1; i--) facinv_[i - 1] = facinv_[i] * i;
}
M fac(int k) const {
assert(0 <= k and k <= n_);
return fac_[k];
}
M facinv(int k) const {
assert(0 <= k and k <= n_);
return facinv_[k];
}
M inv(int k) const {
assert(1 <= k and k <= n_);
return facinv_[k] * fac_[k - 1];
}
M P(int n, int k) const {
if (k < 0 or k > n) return M(0);
assert(n <= n_);
return fac_[n] * facinv_[n - k];
}
M C(int n, int k) const {
if (k < 0 or k > n) return M(0);
assert(n <= n_);
return fac_[n] * facinv_[n - k] * facinv_[k];
}
/**
* @note H(n, k) = (n 個 のボールを k 個の箱に分ける方法の数)
* @note H(n, k) = C(n + k - 1, n)
*/
M H(int n, int k) const {
if (n == 0 and k == 0) return M(1);
return C(n + k - 1, n);
}
M catalan(int n) const {
if (n == 0) return M(1);
return C(2 * n, n) - C(2 * n, n - 1);
}
private:
int n_;
std::vector<M> fac_, facinv_;
};
#line 2 "library-cpp/mod/convolution998244353.hpp"
#line 5 "library-cpp/mod/convolution998244353.hpp"
namespace internal {
// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
template <class mint> struct fft_info {
static constexpr int rank2 = 23;
static constexpr int g = 3;
std::array<mint, rank2 + 1> root; // root[i]^(2^i) == 1
std::array<mint, rank2 + 1> iroot; // root[i] * iroot[i] == 1
std::array<mint, rank2 - 1> rate2;
std::array<mint, rank2 - 1> irate2;
std::array<mint, rank2 - 2> rate3;
std::array<mint, rank2 - 2> irate3;
fft_info() {
root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
iroot[rank2] = root[rank2].inv();
for (int i = rank2 - 1; i >= 0; i--) {
root[i] = root[i + 1] * root[i + 1];
iroot[i] = iroot[i + 1] * iroot[i + 1];
}
{
mint prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 2; i++) {
rate2[i] = root[i + 2] * prod;
irate2[i] = iroot[i + 2] * iprod;
prod *= iroot[i + 2];
iprod *= root[i + 2];
}
}
{
mint prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 3; i++) {
rate3[i] = root[i + 3] * prod;
irate3[i] = iroot[i + 3] * iprod;
prod *= iroot[i + 3];
iprod *= root[i + 3];
}
}
}
};
template <class mint> void butterfly(std::vector<mint>& a) {
int n = int(a.size());
int h = internal::ceil_pow2(n);
static const fft_info<mint> info;
int len = 0; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
while (len < h) {
if (h - len == 1) {
int p = 1 << (h - len - 1);
mint rot = 1;
for (int s = 0; s < (1 << len); s++) {
int offset = s << (h - len);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p] * rot;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
if (s + 1 != (1 << len))
rot *= info.rate2[bsf(~(unsigned int)(s))];
}
len++;
} else {
// 4-base
int p = 1 << (h - len - 2);
mint rot = 1, imag = info.root[2];
for (int s = 0; s < (1 << len); s++) {
mint rot2 = rot * rot;
mint rot3 = rot2 * rot;
int offset = s << (h - len);
for (int i = 0; i < p; i++) {
auto mod2 = 1ULL * mint::mod() * mint::mod();
auto a0 = 1ULL * a[i + offset].val();
auto a1 = 1ULL * a[i + offset + p].val() * rot.val();
auto a2 = 1ULL * a[i + offset + 2 * p].val() * rot2.val();
auto a3 = 1ULL * a[i + offset + 3 * p].val() * rot3.val();
auto a1na3imag =
1ULL * mint(a1 + mod2 - a3).val() * imag.val();
auto na2 = mod2 - a2;
a[i + offset] = a0 + a2 + a1 + a3;
a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
}
if (s + 1 != (1 << len))
rot *= info.rate3[bsf(~(unsigned int)(s))];
}
len += 2;
}
}
}
template <class mint> void butterfly_inv(std::vector<mint>& a) {
int n = int(a.size());
int h = internal::ceil_pow2(n);
static const fft_info<mint> info;
int len = h; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
while (len) {
if (len == 1) {
int p = 1 << (h - len);
mint irot = 1;
for (int s = 0; s < (1 << (len - 1)); s++) {
int offset = s << (h - len + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p];
a[i + offset] = l + r;
a[i + offset + p] =
(unsigned long long)(mint::mod() + l.val() - r.val()) *
irot.val();
;
}
if (s + 1 != (1 << (len - 1)))
irot *= info.irate2[bsf(~(unsigned int)(s))];
}
len--;
} else {
// 4-base
int p = 1 << (h - len);
mint irot = 1, iimag = info.iroot[2];
for (int s = 0; s < (1 << (len - 2)); s++) {
mint irot2 = irot * irot;
mint irot3 = irot2 * irot;
int offset = s << (h - len + 2);
for (int i = 0; i < p; i++) {
auto a0 = 1ULL * a[i + offset + 0 * p].val();
auto a1 = 1ULL * a[i + offset + 1 * p].val();
auto a2 = 1ULL * a[i + offset + 2 * p].val();
auto a3 = 1ULL * a[i + offset + 3 * p].val();
auto a2na3iimag =
1ULL *
mint((mint::mod() + a2 - a3) * iimag.val()).val();
a[i + offset] = a0 + a1 + a2 + a3;
a[i + offset + 1 * p] =
(a0 + (mint::mod() - a1) + a2na3iimag) * irot.val();
a[i + offset + 2 * p] =
(a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) *
irot2.val();
a[i + offset + 3 * p] =
(a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) *
irot3.val();
}
if (s + 1 != (1 << (len - 2)))
irot *= info.irate3[bsf(~(unsigned int)(s))];
}
len -= 2;
}
}
}
template <class mint>
std::vector<mint> convolution_fft(std::vector<mint> a, std::vector<mint> b) {
int n = int(a.size()), m = int(b.size());
int z = 1 << internal::ceil_pow2(n + m - 1);
a.resize(z);
internal::butterfly(a);
b.resize(z);
internal::butterfly(b);
for (int i = 0; i < z; i++) {
a[i] *= b[i];
}
internal::butterfly_inv(a);
a.resize(n + m - 1);
mint iz = mint(z).inv();
for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
return a;
}
} // namespace internal
template <class mint>
std::vector<mint> convolution_naive(const std::vector<mint>& a,
const std::vector<mint>& b) {
int n = int(a.size()), m = int(b.size());
std::vector<mint> ans(n + m - 1);
if (n < m) {
for (int j = 0; j < m; j++) {
for (int i = 0; i < n; i++) {
ans[i + j] += a[i] * b[j];
}
}
} else {
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
ans[i + j] += a[i] * b[j];
}
}
}
return ans;
}
template <class mint>
std::vector<mint> convolution(std::vector<mint>&& a, std::vector<mint>&& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
if (std::min(n, m) <= 60) return convolution_naive(a, b);
return internal::convolution_fft(a, b);
}
template <class mint>
std::vector<mint> convolution(const std::vector<mint>& a,
const std::vector<mint>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
if (std::min(n, m) <= 60) return convolution_naive(a, b);
return internal::convolution_fft(a, b);
}
#line 5 "A.cpp"
using mint = ModInt<998244353>;
// using mint = ModInt<1000000007>;
void solve() {
ModCombination<mint> MC(1000000);
INT(N);
STR(S);
vec<mint> A(N), B(N);
rep(i, N) {
if (S[i] == 'n')
A[i] = 1;
else
B[N - 1 - i] = 1;
}
auto C = convolution(A, B);
debug(C);
vec<mint> L(N - 1);
rep(i, N, 2 * N - 1) {
L[i - N] = C[i];
}
rep(i, N - 1) L[i] *= MC.fac(i);
vec<mint> R(N - 1);
rep(i, N - 1) R[i] = MC.facinv(N - 2 - i);
auto X = convolution(L, R);
int ans = 0;
rep(i, N - 2, 2 * N - 3) {
X[i] *= MC.facinv(i - (N - 2));
ans ^= X[i].val();
}
print(ans);
}
int main() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(20);
cerr << fixed << setprecision(7);
int T = 1;
// cin >> T;
for (int test_case = 1; test_case <= T; test_case++) {
// debug(test_case);
solve();
}
}