結果
| 問題 |
No.2794 I Love EDPC-T
|
| コンテスト | |
| ユーザー |
 ecottea
|
| 提出日時 | 2024-05-27 21:30:59 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 476 ms / 3,000 ms |
| コード長 | 6,537 bytes |
| コンパイル時間 | 417 ms |
| コンパイル使用メモリ | 81,876 KB |
| 実行使用メモリ | 115,500 KB |
| 最終ジャッジ日時 | 2024-12-20 21:34:59 |
| 合計ジャッジ時間 | 7,952 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 31 |
ソースコード
# https://judge.yosupo.jp/submission/55648 より拝借しました．
########################### ここから ###########################
# AtCoder Libary v1.4 を python に移植したもの
# https://github.com/atcoder/ac-library/blob/master/atcoder/convolution.hpp
MOD = 998244353
IMAG = 911660635
IIMAG = 86583718
rate2 = (0, 911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601, 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899, 0)
irate2 = (0, 86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235, 0)
rate3 = (0, 372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099, 183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204, 0)
irate3 = (0, 509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500, 771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681, 0)
def butterfly(a):
n = len(a)
h = (n - 1).bit_length()
le = 0
while le < h:
if h - le == 1:
p = 1 << (h - le - 1)
rot = 1
for s in range(1 << le):
offset = s << (h - le)
for i in range(p):
l = a[i + offset]
r = a[i + offset + p] * rot
a[i + offset] = (l + r) % MOD
a[i + offset + p] = (l - r) % MOD
rot *= rate2[(~s & -~s).bit_length()]
rot %= MOD
le += 1
else:
p = 1 << (h - le - 2)
rot = 1
for s in range(1 << le):
rot2 = rot * rot % MOD
rot3 = rot2 * rot % MOD
offset = s << (h - le)
for i in range(p):
a0 = a[i + offset]
a1 = a[i + offset + p] * rot
a2 = a[i + offset + p * 2] * rot2
a3 = a[i + offset + p * 3] * rot3
a1na3imag = (a1 - a3) % MOD * IMAG
a[i + offset] = (a0 + a2 + a1 + a3) % MOD
a[i + offset + p] = (a0 + a2 - a1 - a3) % MOD
a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % MOD
a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % MOD
rot *= rate3[(~s & -~s).bit_length()]
rot %= MOD
le += 2
def butterfly_inv(a):
n = len(a)
h = (n - 1).bit_length()
le = h
while le:
if le == 1:
p = 1 << (h - le)
irot = 1
for s in range(1 << (le - 1)):
offset = s << (h - le + 1)
for i in range(p):
l = a[i + offset]
r = a[i + offset + p]
a[i + offset] = (l + r) % MOD
a[i + offset + p] = (l - r) * irot % MOD
irot *= irate2[(~s & -~s).bit_length()]
irot %= MOD
le -= 1
else:
p = 1 << (h - le)
irot = 1
for s in range(1 << (le - 2)):
irot2 = irot * irot % MOD
irot3 = irot2 * irot % MOD
offset = s << (h - le + 2)
for i in range(p):
a0 = a[i + offset]
a1 = a[i + offset + p]
a2 = a[i + offset + p * 2]
a3 = a[i + offset + p * 3]
a2na3iimag = (a2 - a3) * IIMAG % MOD
a[i + offset] = (a0 + a1 + a2 + a3) % MOD
a[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % MOD
a[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % MOD
a[i + offset + p * 3] = (a0 - a1 - a2na3iimag) * irot3 % MOD
irot *= irate3[(~s & -~s).bit_length()]
irot %= MOD
le -= 2
def multiply(s, t):
n = len(s)
m = len(t)
if min(n, m) <= 60:
a = [0] * (n + m - 1)
for i in range(n):
if i % 8 == 0:
for j in range(m):
a[i + j] += s[i] * t[j]
a[i + j] %= MOD
else:
for j in range(m):
a[i + j] += s[i] * t[j]
return [x % MOD for x in a]
a = s.copy()
b = t.copy()
z = 1 << (n + m - 2).bit_length()
a += [0] * (z - n)
b += [0] * (z - m)
butterfly(a)
butterfly(b)
for i in range(z):
a[i] *= b[i]
a[i] %= MOD
butterfly_inv(a)
a = a[:n + m - 1]
iz = pow(z, MOD - 2, MOD)
return [v * iz % MOD for v in a]
import atexit
import os
import sys
import __pypy__
class Fastio:
def __init__(self):
self.ibuf = bytes()
self.pil = 0
self.pir = 0
self.sb = __pypy__.builders.StringBuilder()
def load(self):
self.ibuf = self.ibuf[self.pil:]
self.ibuf += os.read(0, 131072)
self.pil = 0
self.pir = len(self.ibuf)
def flush(self):
os.write(1, self.sb.build().encode())
def fastin(self):
if self.pir - self.pil < 32:
self.load()
minus = 0
x = 0
while self.ibuf[self.pil] < 45:
self.pil += 1
if self.ibuf[self.pil] == 45:
minus = 1
self.pil += 1
while self.ibuf[self.pil] >= 48:
x = x * 10 + (self.ibuf[self.pil] & 15)
self.pil += 1
if minus:
x = -x
return x
def fastout(self, x):
self.sb.append(str(x))
def fastoutln(self, x):
self.sb.append(str(x))
self.sb.append('\n')
########################### ここまで ###########################
n = int(input())
s = input()
A = []
l = 0
for i in range(n - 1):
if s[i] == '>':
l += 1
else:
A.append(l)
l = 0
A.append(l)
L = len(A)
if L == 1:
print(0)
exit(0)
# 階乗とその逆数
MOD = 998244353
fac = [1] * (2 * n + 1)
for i in range(1, 2 * n + 1):
fac[i] = (fac[i - 1] * i) % MOD
fac_inv = [1] * (2 * n + 1)
fac_inv[2 * n] = pow(fac[2 * n], MOD - 2, MOD)
for i in range(2 * n - 1, 0, -1):
fac_inv[i] = (fac_inv[i + 1] * (i + 1)) % MOD
fs = []
for l in range(L):
a = A[l]
if l < L - 1:
a -= 1
if l > 0:
a -= 1
if a == -2:
print(0)
exit(0)
f = []
for i in range(n + 1):
if a - i + 1 < i:
break
f.append(fac[a - i + 1] * fac_inv[a - 2 * i + 1] % MOD * fac_inv[i] % MOD)
fs.append(f)
b = 1
while b < L:
for i in range(0, L - b, 2 * b):
fs[i] = multiply(fs[i], fs[i + b])
b <<= 1
x = fs[0]
while len(x) < n:
x.append(0)
res = 0
for i in range(L - 1, n):
sgn = -1 if (i - (L - 1)) & 1 else 1
cat = fac[2 * (n - i)] * fac_inv[n - i] % MOD * fac_inv[n - i + 1] % MOD
res += sgn * cat * x[i - (L - 1)]
res %= MOD
print(res)