結果
| 問題 | No.1504 ヌメロニム |
| ユーザー |
👑  hos.lyric
|
| 提出日時 | 2021-05-07 21:46:30 |
| 言語 | D (dmd 2.109.1) |
| 結果 |
AC
|
| 実行時間 | 1,147 ms / 2,000 ms |
| コード長 | 8,650 bytes |
| コンパイル時間 | 894 ms |
| コンパイル使用メモリ | 123,704 KB |
| 実行使用メモリ | 33,064 KB |
| 最終ジャッジ日時 | 2024-06-22 11:16:39 |
| 合計ジャッジ時間 | 22,727 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge1 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 61 |
ソースコード
import std.conv, std.functional, std.range, std.stdio, std.string;import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons;import core.bitop;class EOFException : Throwable { this() { super("EOF"); } }string[] tokens;string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; }int readInt() { return readToken.to!int; }long readLong() { return readToken.to!long; }real readReal() { return readToken.to!real; }bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } }bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } }int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1;(unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; }int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); }int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); }// M: prime, G: primitive rootclass Fft(int M_, int G, int K) {import std.algorithm : reverse;import std.traits : isIntegral;alias M = M_;// 1, 1/4, 1/8, 3/8, 1/16, 5/16, 3/16, 7/16, ...int[] gs;this() {static assert(2 <= K && K <= 30, "Fft: 2 <= K <= 30 must hold");static assert(!((M - 1) & ((1 << K) - 1)), "Fft: 2^K | M - 1 must hold");gs = new int[1 << (K - 1)];gs[0] = 1;long g2 = G, gg = 1;for (int e = (M - 1) >> K; e; e >>= 1) {if (e & 1) gg = (gg * g2) % M;g2 = (g2 * g2) % M;}gs[1 << (K - 2)] = cast(int)(gg);for (int l = 1 << (K - 2); l >= 2; l >>= 1) {gs[l >> 1] = cast(int)((cast(long)(gs[l]) * gs[l]) % M);}assert((cast(long)(gs[1]) * gs[1]) % M == M - 1,"Fft: g^(2^(K-1)) == -1 (mod M) must hold");for (int l = 2; l <= 1 << (K - 2); l <<= 1) {foreach (i; 1 .. l) {gs[l + i] = cast(int)((cast(long)(gs[l]) * gs[i]) % M);}}}void fft(int[] xs) const {const n = cast(int)(xs.length);assert(!(n & (n - 1)), "Fft.fft: |xs| must be a power of two");assert(n <= 1 << K, "Fft.fft: |xs| <= 2^K must hold");for (int l = n; l >>= 1; ) {foreach (i; 0 .. (n >> 1) / l) {const(long) g = gs[i];foreach (j; (i << 1) * l .. (i << 1 | 1) * l) {const t = cast(int)((g * xs[j + l]) % M);if ((xs[j + l] = xs[j] - t) < 0) xs[j + l] += M;if ((xs[j] += t) >= M) xs[j] -= M;}}}}void invFft(int[] xs) const {const n = cast(int)(xs.length);assert(!(n & (n - 1)), "Fft.invFft: |xs| must be a power of two");assert(n <= 1 << K, "Fft.invFft: |xs| <= 2^K must hold");for (int l = 1; l < n; l <<= 1) reverse(xs[l .. l << 1]);for (int l = 1; l < n; l <<= 1) {foreach (i; 0 .. (n >> 1) / l) {const(long) g = gs[i];foreach (j; (i << 1) * l .. (i << 1 | 1) * l) {int t = cast(int)((g * (xs[j] - xs[j + l])) % M);if (t < 0) t += M;if ((xs[j] += xs[j + l]) >= M) xs[j] -= M;xs[j + l] = t;}}}}T[] convolve(T)(inout(T)[] as, inout(T)[] bs) const if (isIntegral!T) {const na = cast(int)(as.length), nb = cast(int)(bs.length);int n, invN = 1;for (n = 1; n < na + nb - 1; n <<= 1) {invN = ((invN & 1) ? (invN + M) : invN) >> 1;}auto xs = new int[n], ys = new int[n];foreach (i; 0 .. na) if ((xs[i] = cast(int)(as[i] % M)) < 0) xs[i] += M;foreach (i; 0 .. nb) if ((ys[i] = cast(int)(bs[i] % M)) < 0) ys[i] += M;fft(xs);fft(ys);foreach (i; 0 .. n) {xs[i] = cast(int)((((cast(long)(xs[i]) * ys[i]) % M) * invN) % M);}invFft(xs);auto cs = new T[na + nb - 1];foreach (i; 0 .. na + nb - 1) cs[i] = cast(T)(xs[i]);return cs;}ModInt!M[] convolve(inout(ModInt!M)[] as, inout(ModInt!M)[] bs) const {const na = cast(int)(as.length), nb = cast(int)(bs.length);int n, invN = 1;for (n = 1; n < na + nb - 1; n <<= 1) {invN = ((invN & 1) ? (invN + M) : invN) >> 1;}auto xs = new int[n], ys = new int[n];foreach (i; 0 .. na) xs[i] = as[i].x;foreach (i; 0 .. nb) ys[i] = bs[i].x;fft(xs);fft(ys);foreach (i; 0 .. n) {xs[i] = cast(int)((((cast(long)(xs[i]) * ys[i]) % M) * invN) % M);}invFft(xs);auto cs = new ModInt!M[na + nb - 1];foreach (i; 0 .. na + nb - 1) cs[i].x = xs[i];return cs;}int[] convolve(int M1)(inout(ModInt!M1)[] as, inout(ModInt!M1)[] bs) constif (M != M1) {const na = cast(int)(as.length), nb = cast(int)(bs.length);int n, invN = 1;for (n = 1; n < na + nb - 1; n <<= 1) {invN = ((invN & 1) ? (invN + M) : invN) >> 1;}auto xs = new int[n], ys = new int[n];foreach (i; 0 .. na) xs[i] = as[i].x;foreach (i; 0 .. nb) ys[i] = bs[i].x;fft(xs);fft(ys);foreach (i; 0 .. n) {xs[i] = cast(int)((((cast(long)(xs[i]) * ys[i]) % M) * invN) % M);}invFft(xs);return xs[0 .. na + nb - 1];}}alias Fft0 = Fft!(998244353, 3, 20);struct ModInt(int M_) {import std.conv : to;alias M = M_;int x;this(ModInt a) { x = a.x; }this(long a) { x = cast(int)(a % M); if (x < 0) x += M; }ref ModInt opAssign(long a) { return (this = ModInt(a)); }ref ModInt opOpAssign(string op)(ModInt a) {static if (op == "+") { x += a.x; if (x >= M) x -= M; }else static if (op == "-") { x -= a.x; if (x < 0) x += M; }else static if (op == "*") { x = cast(int)((cast(long)(x) * a.x) % M); }else static if (op == "/") { this *= a.inv(); }else static assert(false);return this;}ref ModInt opOpAssign(string op)(long a) {static if (op == "^^") {if (a < 0) return (this = inv()^^(-a));ModInt t2 = this, te = ModInt(1);for (long e = a; e > 0; e >>= 1) {if (e & 1) te *= t2;t2 *= t2;}x = cast(int)(te.x);return this;} else return mixin("this " ~ op ~ "= ModInt(a)");}ModInt inv() const {int a = x, b = M, 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;}}ModInt opUnary(string op: "-")() const { return ModInt(-x); }ModInt opBinary(string op, T)(T a) const {return mixin("ModInt(this) " ~ op ~ "= a");}ModInt opBinaryRight(string op)(long a) const {return mixin("ModInt(a) " ~ op ~ "= this");}bool opCast(T: bool)() const { return (x != 0); }string toString() const { return x.to!string; }}enum MO = 998244353;alias Mint = ModInt!MO;enum LIM = 600_010;Mint[] inv, fac, invFac;void prepare() {inv = new Mint[LIM];fac = new Mint[LIM];invFac = new Mint[LIM];inv[1] = 1;foreach (i; 2 .. LIM) {inv[i] = -(Mint.M / i) * inv[cast(size_t)(Mint.M % i)];}fac[0] = invFac[0] = 1;foreach (i; 1 .. LIM) {fac[i] = fac[i - 1] * i;invFac[i] = invFac[i - 1] * inv[i];}}Mint binom(long n, long k) {if (0 <= k && k <= n) {assert(n < LIM);return fac[cast(size_t)(n)] * invFac[cast(size_t)(k)] * invFac[cast(size_t)(n - k)];} else {return Mint(0);}}void main() {prepare;const FFT = new Fft0;try {for (; ; ) {const N = readInt();const S = readToken();auto fs = new Mint[N + 1];auto gs = new Mint[N + 1];foreach (i; 0 .. N) {if (S[i] == 'n') fs[i] += 1;if (S[i] == 'i') gs[N - i] += 1;}const hs = FFT.convolve(fs, gs);debug {writeln("fs = ", fs);writeln("gs = ", gs);writeln("hs = ", hs);}auto ps = new Mint[N + 1];auto qs = new Mint[N + 1];foreach (i; 0 .. N) {ps[i] = fac[i] * hs[N + i + 1];qs[N - i] = invFac[i];}const rs = FFT.convolve(ps, qs);debug {writeln("ps = ", ps);writeln("qs = ", qs);writeln("rs = ", rs);}uint ans;foreach (i; 0 .. N) {const here = invFac[i] * rs[N + i];debug {writeln(i, ": ", here);}ans ^= here.x;}writeln(ans);}} catch (EOFException e) {}}