結果
| 問題 |
No.2794 I Love EDPC-T
|
| コンテスト | |
| ユーザー |
 ecottea
|
| 提出日時 | 2024-05-26 20:38:42 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 10,882 bytes |
| コンパイル時間 | 370 ms |
| コンパイル使用メモリ | 81,920 KB |
| 実行使用メモリ | 323,300 KB |
| 最終ジャッジ日時 | 2024-12-20 21:27:14 |
| 合計ジャッジ時間 | 37,289 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 26 TLE * 5 |
ソースコード
# https://github.com/not522/ac-library-python
import typing
def _ceil_pow2(n: int) -> int:
x = 0
while (1 << x) < n:
x += 1
return x
def _bsf(n: int) -> int:
x = 0
while n % 2 == 0:
x += 1
n //= 2
return x
def _is_prime(n: int) -> bool:
'''
Reference:
M. Forisek and J. Jancina,
Fast Primality Testing for Integers That Fit into a Machine Word
'''
if n <= 1:
return False
if n == 2 or n == 7 or n == 61:
return True
if n % 2 == 0:
return False
d = n - 1
while d % 2 == 0:
d //= 2
for a in (2, 7, 61):
t = d
y = pow(a, t, n)
while t != n - 1 and y != 1 and y != n - 1:
y = y * y % n
t <<= 1
if y != n - 1 and t % 2 == 0:
return False
return True
def _inv_gcd(a: int, b: int) -> typing.Tuple[int, int]:
a %= b
if a == 0:
return (b, 0)
# Contracts:
# [1] s - m0 * a = 0 (mod b)
# [2] t - m1 * a = 0 (mod b)
# [3] s * |m1| + t * |m0| <= b
s = b
t = a
m0 = 0
m1 = 1
while t:
u = s // t
s -= t * u
m0 -= m1 * u # |m1 * u| <= |m1| * s <= b
# [3]:
# (s - t * u) * |m1| + t * |m0 - m1 * u|
# <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
# = s * |m1| + t * |m0| <= b
s, t = t, s
m0, m1 = m1, m0
# by [3]: |m0| <= b/g
# by g != b: |m0| < b/g
if m0 < 0:
m0 += b // s
return (s, m0)
def _primitive_root(m: int) -> int:
if m == 2:
return 1
if m == 167772161:
return 3
if m == 469762049:
return 3
if m == 754974721:
return 11
if m == 998244353:
return 3
divs = [2] + [0] * 19
cnt = 1
x = (m - 1) // 2
while x % 2 == 0:
x //= 2
i = 3
while i * i <= x:
if x % i == 0:
divs[cnt] = i
cnt += 1
while x % i == 0:
x //= i
i += 2
if x > 1:
divs[cnt] = x
cnt += 1
g = 2
while True:
for i in range(cnt):
if pow(g, (m - 1) // divs[i], m) == 1:
break
else:
return g
g += 1
class ModContext:
context: typing.List[int] = []
def __init__(self, mod: int) -> None:
assert 1 <= mod
self.mod = mod
def __enter__(self) -> None:
self.context.append(self.mod)
def __exit__(self, exc_type: typing.Any, exc_value: typing.Any,
traceback: typing.Any) -> None:
self.context.pop()
@classmethod
def get_mod(cls) -> int:
return cls.context[-1]
class Modint:
def __init__(self, v: int = 0) -> None:
self._mod = ModContext.get_mod()
if v == 0:
self._v = 0
else:
self._v = v % self._mod
def mod(self) -> int:
return self._mod
def val(self) -> int:
return self._v
def __iadd__(self, rhs: typing.Union['Modint', int]) -> 'Modint':
if isinstance(rhs, Modint):
self._v += rhs._v
else:
self._v += rhs
if self._v >= self._mod:
self._v -= self._mod
return self
def __isub__(self, rhs: typing.Union['Modint', int]) -> 'Modint':
if isinstance(rhs, Modint):
self._v -= rhs._v
else:
self._v -= rhs
if self._v < 0:
self._v += self._mod
return self
def __imul__(self, rhs: typing.Union['Modint', int]) -> 'Modint':
if isinstance(rhs, Modint):
self._v = self._v * rhs._v % self._mod
else:
self._v = self._v * rhs % self._mod
return self
def __ifloordiv__(self, rhs: typing.Union['Modint', int]) -> 'Modint':
if isinstance(rhs, Modint):
inv = rhs.inv()._v
else:
inv = atcoder._math._inv_gcd(rhs, self._mod)[1]
self._v = self._v * inv % self._mod
return self
def __pos__(self) -> 'Modint':
return self
def __neg__(self) -> 'Modint':
return Modint() - self
def __pow__(self, n: int) -> 'Modint':
assert 0 <= n
return Modint(pow(self._v, n, self._mod))
def inv(self) -> 'Modint':
eg = _inv_gcd(self._v, self._mod)
assert eg[0] == 1
return Modint(eg[1])
def __add__(self, rhs: typing.Union['Modint', int]) -> 'Modint':
if isinstance(rhs, Modint):
result = self._v + rhs._v
if result >= self._mod:
result -= self._mod
return raw(result)
else:
return Modint(self._v + rhs)
def __sub__(self, rhs: typing.Union['Modint', int]) -> 'Modint':
if isinstance(rhs, Modint):
result = self._v - rhs._v
if result < 0:
result += self._mod
return raw(result)
else:
return Modint(self._v - rhs)
def __mul__(self, rhs: typing.Union['Modint', int]) -> 'Modint':
if isinstance(rhs, Modint):
return Modint(self._v * rhs._v)
else:
return Modint(self._v * rhs)
def __floordiv__(self, rhs: typing.Union['Modint', int]) -> 'Modint':
if isinstance(rhs, Modint):
inv = rhs.inv()._v
else:
inv = _inv_gcd(rhs, self._mod)[1]
return Modint(self._v * inv)
def __eq__(self, rhs: typing.Union['Modint', int]) -> bool: # type: ignore
if isinstance(rhs, Modint):
return self._v == rhs._v
else:
return self._v == rhs
def __ne__(self, rhs: typing.Union['Modint', int]) -> bool: # type: ignore
if isinstance(rhs, Modint):
return self._v != rhs._v
else:
return self._v != rhs
def raw(v: int) -> Modint:
x = Modint()
x._v = v
return x
_sum_e = {} # _sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
def _butterfly(a: typing.List[Modint]) -> None:
g = _primitive_root(a[0].mod())
n = len(a)
h = _ceil_pow2(n)
if a[0].mod() not in _sum_e:
es = [Modint(0)] * 30 # es[i]^(2^(2+i)) == 1
ies = [Modint(0)] * 30
cnt2 = _bsf(a[0].mod() - 1)
e = Modint(g) ** ((a[0].mod() - 1) >> cnt2)
ie = e.inv()
for i in range(cnt2, 1, -1):
# e^(2^i) == 1
es[i - 2] = e
ies[i - 2] = ie
e = e * e
ie = ie * ie
sum_e = [Modint(0)] * 30
now = Modint(1)
for i in range(cnt2 - 2):
sum_e[i] = es[i] * now
now *= ies[i]
_sum_e[a[0].mod()] = sum_e
else:
sum_e = _sum_e[a[0].mod()]
for ph in range(1, h + 1):
w = 1 << (ph - 1)
p = 1 << (h - ph)
now = Modint(1)
for s in range(w):
offset = s << (h - ph + 1)
for i in range(p):
left = a[i + offset]
right = a[i + offset + p] * now
a[i + offset] = left + right
a[i + offset + p] = left - right
now *= sum_e[_bsf(~s)]
_sum_ie = {} # _sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
def _butterfly_inv(a: typing.List[Modint]) -> None:
g = _primitive_root(a[0].mod())
n = len(a)
h = _ceil_pow2(n)
if a[0].mod() not in _sum_ie:
es = [Modint(0)] * 30 # es[i]^(2^(2+i)) == 1
ies = [Modint(0)] * 30
cnt2 = _bsf(a[0].mod() - 1)
e = Modint(g) ** ((a[0].mod() - 1) >> cnt2)
ie = e.inv()
for i in range(cnt2, 1, -1):
# e^(2^i) == 1
es[i - 2] = e
ies[i - 2] = ie
e = e * e
ie = ie * ie
sum_ie = [Modint(0)] * 30
now = Modint(1)
for i in range(cnt2 - 2):
sum_ie[i] = ies[i] * now
now *= es[i]
_sum_ie[a[0].mod()] = sum_ie
else:
sum_ie = _sum_ie[a[0].mod()]
for ph in range(h, 0, -1):
w = 1 << (ph - 1)
p = 1 << (h - ph)
inow = Modint(1)
for s in range(w):
offset = s << (h - ph + 1)
for i in range(p):
left = a[i + offset]
right = a[i + offset + p]
a[i + offset] = left + right
a[i + offset + p] = Modint(
(a[0].mod() + left.val() - right.val()) * inow.val())
inow *= sum_ie[_bsf(~s)]
def convolution_mod(a: typing.List[Modint],
b: typing.List[Modint]) -> typing.List[Modint]:
n = len(a)
m = len(b)
if n == 0 or m == 0:
return []
if min(n, m) <= 60:
if n < m:
n, m = m, n
a, b = b, a
ans = [Modint(0) for _ in range(n + m - 1)]
for i in range(n):
for j in range(m):
ans[i + j] += a[i] * b[j]
return ans
z = 1 << _ceil_pow2(n + m - 1)
while len(a) < z:
a.append(Modint(0))
_butterfly(a)
while len(b) < z:
b.append(Modint(0))
_butterfly(b)
for i in range(z):
a[i] *= b[i]
_butterfly_inv(a)
a = a[:n + m - 1]
iz = Modint(z).inv()
for i in range(n + m - 1):
a[i] *= iz
return a
def convolution(mod: int, a: typing.List[typing.Any],
b: typing.List[typing.Any]) -> typing.List[typing.Any]:
n = len(a)
m = len(b)
if n == 0 or m == 0:
return []
with ModContext(mod):
a2 = list(map(Modint, a))
b2 = list(map(Modint, b))
return list(map(lambda c: c.val(), convolution_mod(a2, b2)))
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] = convolution(MOD, 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)