結果

問題 No.2794 I Love EDPC-T
ユーザー ecotteaecottea
提出日時 2024-05-27 21:30:59
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 448 ms / 3,000 ms
コード長 6,537 bytes
コンパイル時間 2,743 ms
コンパイル使用メモリ 82,100 KB
実行使用メモリ 115,604 KB
最終ジャッジ日時 2024-05-30 19:04:45
合計ジャッジ時間 7,661 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
このコードへのチャレンジ
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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 40 ms
53,684 KB
testcase_01 AC 38 ms
54,288 KB
testcase_02 AC 38 ms
54,420 KB
testcase_03 AC 39 ms
54,468 KB
testcase_04 AC 39 ms
54,216 KB
testcase_05 AC 39 ms
54,972 KB
testcase_06 AC 58 ms
67,676 KB
testcase_07 AC 65 ms
70,772 KB
testcase_08 AC 69 ms
72,984 KB
testcase_09 AC 38 ms
54,720 KB
testcase_10 AC 37 ms
53,908 KB
testcase_11 AC 39 ms
54,352 KB
testcase_12 AC 38 ms
54,344 KB
testcase_13 AC 205 ms
88,596 KB
testcase_14 AC 136 ms
78,156 KB
testcase_15 AC 212 ms
88,696 KB
testcase_16 AC 226 ms
102,392 KB
testcase_17 AC 245 ms
101,544 KB
testcase_18 AC 244 ms
106,400 KB
testcase_19 AC 233 ms
102,120 KB
testcase_20 AC 143 ms
96,240 KB
testcase_21 AC 317 ms
114,076 KB
testcase_22 AC 321 ms
114,164 KB
testcase_23 AC 323 ms
114,520 KB
testcase_24 AC 320 ms
113,724 KB
testcase_25 AC 332 ms
114,044 KB
testcase_26 AC 44 ms
61,896 KB
testcase_27 AC 67 ms
84,284 KB
testcase_28 AC 189 ms
115,604 KB
testcase_29 AC 163 ms
109,044 KB
testcase_30 AC 448 ms
114,028 KB
testcase_31 AC 437 ms
108,484 KB
testcase_32 AC 352 ms
107,152 KB
testcase_33 AC 348 ms
112,764 KB
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ソースコード

diff # 

# 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)
0