結果
| 問題 | No.2386 Udon Coupon (Easy) |
| ユーザー |
 Iorn
|
| 提出日時 | 2023-07-21 23:53:38 |
| 言語 | Python3 (3.12.2 + numpy 1.26.4 + scipy 1.12.0) |
| 結果 |
AC
|
| 実行時間 | 373 ms / 2,000 ms |
| コード長 | 39,149 bytes |
| コンパイル時間 | 158 ms |
| コンパイル使用メモリ | 16,768 KB |
| 実行使用メモリ | 23,296 KB |
| 最終ジャッジ日時 | 2024-09-22 01:18:25 |
| 合計ジャッジ時間 | 9,604 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
（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 | 58 ms
15,488 KB |
| testcase_01 | AC | 55 ms
15,488 KB |
| testcase_02 | AC | 56 ms
15,616 KB |
| testcase_03 | AC | 58 ms
15,488 KB |
| testcase_04 | AC | 54 ms
15,744 KB |
| testcase_05 | AC | 56 ms
15,744 KB |
| testcase_06 | AC | 59 ms
15,616 KB |
| testcase_07 | AC | 371 ms
23,296 KB |
| testcase_08 | AC | 58 ms
15,616 KB |
| testcase_09 | AC | 61 ms
15,616 KB |
| testcase_10 | AC | 136 ms
17,408 KB |
| testcase_11 | AC | 92 ms
16,128 KB |
| testcase_12 | AC | 292 ms
21,248 KB |
| testcase_13 | AC | 356 ms
22,912 KB |
| testcase_14 | AC | 321 ms
22,016 KB |
| testcase_15 | AC | 351 ms
22,912 KB |
| testcase_16 | AC | 274 ms
20,864 KB |
| testcase_17 | AC | 338 ms
22,272 KB |
| testcase_18 | AC | 175 ms
18,304 KB |
| testcase_19 | AC | 80 ms
15,872 KB |
| testcase_20 | AC | 261 ms
20,352 KB |
| testcase_21 | AC | 326 ms
22,144 KB |
| testcase_22 | AC | 220 ms
19,584 KB |
| testcase_23 | AC | 203 ms
18,944 KB |
| testcase_24 | AC | 106 ms
16,640 KB |
| testcase_25 | AC | 249 ms
19,968 KB |
| testcase_26 | AC | 331 ms
21,888 KB |
| testcase_27 | AC | 355 ms
23,168 KB |
| testcase_28 | AC | 205 ms
19,328 KB |
| testcase_29 | AC | 142 ms
17,280 KB |
| testcase_30 | AC | 72 ms
16,000 KB |
| testcase_31 | AC | 193 ms
18,816 KB |
| testcase_32 | AC | 80 ms
15,872 KB |
| testcase_33 | AC | 372 ms
23,296 KB |
| testcase_34 | AC | 217 ms
19,328 KB |
| testcase_35 | AC | 290 ms
20,992 KB |
| testcase_36 | AC | 373 ms
22,784 KB |
| testcase_37 | AC | 291 ms
21,376 KB |
| testcase_38 | AC | 237 ms
19,712 KB |
| testcase_39 | AC | 183 ms
18,688 KB |
ソースコード
import time
from typing import Generic, Iterable, Iterator, TypeVar, Optional, List
from array import array
from bisect import bisect_left, bisect_right, insort
import collections
import copy
import heapq
import itertools
import decimal
from decimal import Decimal
import math
import string
import sys
sys.setrecursionlimit(10**6)
def I(): return int(sys.stdin.readline().rstrip())
def MI(): return map(int, sys.stdin.readline().rstrip().split())
def LI(): return list(map(int, sys.stdin.readline().rstrip().split()))
def LII(H): return [list(map(int, sys.stdin.readline().rstrip().split())) for _ in range(H)]
def ST(): return sys.stdin.readline().rstrip()
def SS(H): return [ST() for _ in range(H)]
def LS(): return list(sys.stdin.readline().rstrip().split())
def ARRAY(L): return array("i", L)
INF = (1 << 63)-1
DIFF = 10 ** -9
DX = [1, 0, -1, 0, 1, 1, -1, -1]
DY = [0, 1, 0, -1, 1, -1, 1, -1]
MOD = 998244353
# 累積和 ans=list(itertools.accumulate(L))
# 順列 ans=list(itertools.permutation(L))
# 直積 ans=list(itertools.product(L,M))
# 重複なし組み合わせ ans=list(itertools.combinations(L,2))
# 重複あり組み合わせ ans=list(itertools.combinations_with_replacement(L,2))
# nCr ans=math.comb(n,r)
# 日付を比較
def compare_date(date1, date2):
# date = "2019/04/30"
formatted_date1 = time.strptime(date1, "%Y/%m/%d")
formatted_date2 = time.strptime(date2, "%Y/%m/%d")
return formatted_date1 < formatted_date2
# 四捨五入
def half_up(x):
return Decimal(x).quantize(Decimal('1'), rounding=decimal.ROUND_HALF_UP)
# 切り上げ
def ceiling(x):
return Decimal(x).quantize(Decimal('0.1'), rounding=decimal.ROUND_CEILING)
# 切り捨て
def floor(x):
return Decimal(x).quantize(Decimal('0.1'), rounding=decimal.ROUND_FLOOR)
# Nまでの数を素数かどうか判定（エラトステネスのふるい）
def prime_judge(n: int):
is_prime = [True] * (n + 1)
is_prime[0], is_prime[1] = False, False
for i in range(2, int(math.sqrt(n)) + 1):
if is_prime[i]:
for j in range(2 * i, n + 1, i):
is_prime[j] = False
return is_prime
# 素因数分解
def prime_factorization(N: int):
arr = []
sqrt = int(math.sqrt(N))
for i in range(2, sqrt+1):
if N % i == 0:
cnt = 0
while N % i == 0:
cnt += 1
N //= i
arr.append([i, cnt])
if N != 1:
arr.append([N, 1])
return arr
# 1文字ずつ文字列をずらしたときの最長共通接頭辞の長さ
def z_algorithm(S: string):
n = len(S)
rtn = [-1]*n
rtn[0] = n
i, j = 1, 0
while i < len(S):
while i+j < len(S) and S[j] == S[i+j]:
j += 1
rtn[i] = j
if j == 0:
i += 1
k = 1
while i+k < len(S) and k+rtn[k] < j:
rtn[i+k] = rtn[k]
k += 1
i += k
j -= k
return rtn
# Nまでの積をxで何回割り切れるか
def divide_num(N: int, x: int):
rtn = 0
i = 1
while pow(x, i) <= N:
rtn += N//pow(x, i)
i += 1
return rtn
# 拡張ユークリッド互除法
def xgcd(a, b):
x0, y0, x1, y1 = 1, 0, 0, 1
while b != 0:
q, a, b = a//b, b, a % b
x0, x1 = x1, x0-q*x1
y0, y1 = y1, y0-q*y1
return a, x0, y0
# 逆元を求める
def modinv(a, mod=MOD):
g, x, y = xgcd(a, mod)
if g != 1:
raise Exception("moduler inverse does not exist")
else:
return x % mod
# combinationの逆元を求める
def combination_modinv(n, r, mod=MOD):
if n < 0 or r < 0 or n < r:
return 0
fact = [1]*(n+2)
fact_inv = [1]*(n+2)
for i in range(1, n+2):
fact[i] = (fact[i-1]*i) % mod
fact_inv[n+1] = pow(fact[n+1], mod-2, mod)
for i in range(n, -1, -1):
fact_inv[i] = (fact_inv[i+1]*(i+1)) % mod
return (fact[n]*fact_inv[r] % mod)*fact_inv[n-r] % mod
class BIT:
# 長さN+1の配列を初期化
def __init__(self, N):
self.size = N
self.bit = [0]*(N+1)
# i番目までの和を求める
def sum(self, i):
res = 0
while i > 0:
res += self.bit[i] # フェニック木のi番目の値を加算
i -= -i & i # 最も右にある1の桁を0にする
return res
# i番目の値にxを足して更新する
def add(self, i, x):
while i <= self.size:
self.bit[i] += x # フェニック木のi番目にxを足して更新
i += -i & i # 最も右にある1の桁に1を足す
# N mod p = a, N mod q = b
# px + a = qy + b
# px - qy = b-a
# px = 1 mod q
def crp(a, p, b, q):
x = pow(p, -1, q)
x *= b-a
x %= q
return p*x + a
def Dijkstra(edges, num_node):
""" 経路の表現
[終点, 辺の値]
A, B, C, D, ... → 0, 1, 2, ...とする """
node = [float('inf')] * num_node # スタート地点以外の値は∞で初期化
node[0] = 0 # スタートは0で初期化
node_name = [i for i in range(num_node)] # ノードの名前を0~ノードの数で表す
while len(node_name) > 0:
r = node_name[0]
# 最もコストが小さい頂点を探す
for i in node_name:
if node[i] < node[r]:
r = i # コストが小さい頂点が見つかると更新
# 最もコストが小さい頂点を取り出す
min_point = node_name.pop(node_name.index(r))
# 経路の要素を各変数に格納することで，視覚的に見やすくする
for factor in edges[min_point]:
goal = factor[0] # 終点
cost = factor[1] # コスト
# 更新条件
if node[min_point] + cost < node[goal]:
node[goal] = node[min_point] + cost # 更新
return node
# 行きがけ、帰りがけの順番を取得
def EulerTour(n, graph, root):
"""
(n: int, graph: List[List[int]], root: int) -> Tuple[List[int], List[int], List[int]]:
:param n: the number of vertex points
:param graph: 2D matrix of N vertices given by the edges
:param root: start node index
:return tour: order of visited vertex
:return in_time: first visiting time of each vertex
:return out_time: last visiting time of each vertex
example:
graph = [[] for _ in range(n)]
for _ in range(n):
a, b = map(int, input().split())
graph[a].append(b)
graph[b].append(a)
tour, in_time, out_time = EulerTour(n, graph, 0)
"""
parent = [-1] * n
stack = [~root, root] # postorder, preorder
curr_time = -1
tour = []
in_time = [-1] * n
out_time = [-1] * n
while stack:
curr_node = stack.pop()
curr_time += 1
if curr_node >= 0: # preorder
tour.append(curr_node)
if in_time[curr_node] == -1:
in_time[curr_node] = curr_time
for next_node in graph[curr_node]:
if next_node != parent[curr_node]:
parent[next_node] = curr_node
stack.append(~next_node)
stack.append(next_node)
elif curr_node < 0: # postorder
out_time[~curr_node] = curr_time
if parent[~curr_node] != -1:
tour.append(parent[~curr_node])
return tour, in_time, out_time
class UnionFind():
def __init__(self, n):
self.n = n
self.parents = [-1] * n
def find(self, x):
if self.parents[x] < 0:
return x
else:
self.parents[x] = self.find(self.parents[x])
return self.parents[x]
def union(self, x, y):
x = self.find(x)
y = self.find(y)
if x == y:
return
if self.parents[x] > self.parents[y]:
x, y = y, x
self.parents[x] += self.parents[y]
self.parents[y] = x
def size(self, x):
return -self.parents[self.find(x)]
def same(self, x, y):
return self.find(x) == self.find(y)
def members(self, x):
root = self.find(x)
return [i for i in range(self.n) if self.find(i) == root]
def roots(self):
return [i for i, x in enumerate(self.parents) if x < 0]
def group_count(self):
return len(self.roots())
def all_group_members(self):
group_members = collections.defaultdict(list)
for member in range(self.n):
group_members[self.find(member)].append(member)
return group_members
def __str__(self):
return '\n'.join(f'{r}: {m}' for r, m in self.all_group_members().items())
def make_kmp_table(t):
i = 2
j = 0
m = len(t)
tbl = [0] * (m + 1)
tbl[0] = -1
while i <= m:
if t[i - 1] == t[j]:
tbl[i] = j + 1
i += 1
j += 1
elif j > 0:
j = tbl[j]
else:
tbl[i] = 0
i += 1
return tbl
# 文字列Sの中に文字列Tが存在するかどうか
def kmp(s, t):
matched_indices = []
tbl = make_kmp_table(t)
i = 0
j = 0
n = len(s)
m = len(t)
while i + j < n:
if t[j] == s[i + j]:
j += 1
if j == m:
matched_indices.append(i)
i += j - tbl[j]
j = tbl[j]
else:
i += j - tbl[j]
if j > 0:
j = tbl[j]
return matched_indices
# 強連結成分分解
class SCC:
def __init__(self, n):
self.n = n
self.graph = [[] for _ in range(n)]
self.rev_graph = [[] for _ in range(n)]
self.labels = [-1] * n
self.lb_cnt = 0
def add_edge(self, v, nxt_v):
self.graph[v].append(nxt_v)
self.rev_graph[nxt_v].append(v)
def build(self):
self.post_order = []
self.used = [False] * self.n
for v in range(self.n):
if not self.used[v]:
self._dfs(v)
for v in reversed(self.post_order):
if self.labels[v] == -1:
self._rev_dfs(v)
self.lb_cnt += 1
def _dfs(self, v):
stack = [v, 0]
while stack:
v, idx = stack[-2:]
if not idx and self.used[v]:
stack.pop()
stack.pop()
else:
self.used[v] = True
if idx < len(self.graph[v]):
stack[-1] += 1
stack.append(self.graph[v][idx])
stack.append(0)
else:
stack.pop()
self.post_order.append(stack.pop())
def _rev_dfs(self, v):
stack = [v]
self.labels[v] = self.lb_cnt
while stack:
v = stack.pop()
for nxt_v in self.rev_graph[v]:
if self.labels[nxt_v] != -1:
continue
stack.append(nxt_v)
self.labels[nxt_v] = self.lb_cnt
def construct(self):
self.dag = [[] for i in range(self.lb_cnt)]
self.groups = [[] for i in range(self.lb_cnt)]
for v, lb in enumerate(self.labels):
for nxt_v in self.graph[v]:
nxt_lb = self.labels[nxt_v]
if lb == nxt_lb:
continue
self.dag[lb].append(nxt_lb)
self.groups[lb].append(v)
return self.dag, self.groups
class SegTree:
""" 点代入/区間総和
操作 segfunc 単位元
最小値 min(x, y) float('inf')
最大値 max(x, y) -float('inf')
区間和 x + y 0
区間積 x * y 1
最大公約数 math.gcd(x, y) 0
segfunc : 和の計算がデフォ、最小値・最大値などのモノイドに置換
add : k番目の値にxを加算
update : k番目の値をxに更新
query : 区間[l,r)のseg_funcモノイドの結果を出力
"""
def __init__(self, init_val: list, ide_ele: int = 0):
n = len(init_val)
self.ide_ele = ide_ele
self.num = 1 << (n-1).bit_length()
self.tree = [ide_ele]*2*self.num
for i in range(n):
self.tree[self.num+i] = init_val[i]
for i in range(self.num-1, 0, -1):
self.tree[i] = self.segfunc(self.tree[2*i], self.tree[2*i+1])
def segfunc(x, y):
return x+y
def add(self, k, x):
k += self.num
self.tree[k] += x
while k > 1:
self.tree[k >> 1] = self.segfunc(self.tree[k], self.tree[k ^ 1])
k >>= 1
def update(self, k, x):
k += self.num
self.tree[k] = x
while k > 1:
self.tree[k >> 1] = self.segfunc(self.tree[k], self.tree[k ^ 1])
k >>= 1
def query(self, l, r):
res = self.ide_ele
l += self.num
r += self.num
while l < r:
if l & 1:
res = self.segfunc(res, self.tree[l])
l += 1
if r & 1:
res = self.segfunc(res, self.tree[r-1])
l >>= 1
r >>= 1
return res
class LazySegTree_RAQ:
""" 区間代入/区間総和
seg_func : 和の計算がデフォ、最小値・最大値などのモノイドに置換
add : 区間[l,r)の値にxを加算
query : 区間[l,r)のseg_funcモノイドの結果を出力
"""
def __init__(self, init_val, segfunc=None, ide_ele: int = 0):
n = len(init_val)
self.ide_ele = ide_ele
if segfunc is not None:
self.segfunc = segfunc
self.num = 1 << (n-1).bit_length()
self.tree = [ide_ele]*2*self.num
self.lazy = [0]*2*self.num
for i in range(n):
self.tree[self.num+i] = init_val[i]
for i in range(self.num-1, 0, -1):
self.tree[i] = self.segfunc(self.tree[2*i], self.tree[2*i+1])
def segfunc(x, y):
return x+y
def gindex(self, l, r):
l += self.num
r += self.num
lm = l >> (l & -l).bit_length()
rm = r >> (r & -r).bit_length()
while r > l:
if l <= lm:
yield l
if r <= rm:
yield r
r >>= 1
l >>= 1
while l:
yield l
l >>= 1
def propagates(self, *ids):
for i in reversed(ids):
v = self.lazy[i]
if v == 0:
continue
self.lazy[i] = 0
self.lazy[2*i] += v
self.lazy[2*i+1] += v
self.tree[2*i] += v
self.tree[2*i+1] += v
def add(self, l, r, x):
ids = self.gindex(l, r)
l += self.num
r += self.num
while l < r:
if l & 1:
self.lazy[l] += x
self.tree[l] += x
l += 1
if r & 1:
self.lazy[r-1] += x
self.tree[r-1] += x
r >>= 1
l >>= 1
for i in ids:
self.tree[i] = self.segfunc(self.tree[2*i], self.tree[2*i+1]) + self.lazy[i]
def query(self, l, r):
self.propagates(*self.gindex(l, r))
res = self.ide_ele
l += self.num
r += self.num
while l < r:
if l & 1:
res = self.segfunc(res, self.tree[l])
l += 1
if r & 1:
res = self.segfunc(res, self.tree[r-1])
l >>= 1
r >>= 1
return res
class LazySegTree_RUQ:
""" 区間代入/区間総和
seg_func : 和の計算がデフォ、最小値・最大値などのモノイドに置換
update : 区間[l,r)の値をxに加算
query : 区間[l,r)のseg_funcモノイドの結果を出力
"""
def __init__(self, init_val: list, segfunc=None, ide_ele: int = 0):
n = len(init_val)
self.ide_ele = ide_ele
self.num = 1 << (n-1).bit_length()
if segfunc is not None:
self.segfunc = segfunc
self.tree = [ide_ele]*2*self.num
self.lazy = [None]*2*self.num
for i in range(n):
self.tree[self.num+i] = init_val[i]
for i in range(self.num-1, 0, -1):
self.tree[i] = self.segfunc(self.tree[2*i], self.tree[2*i+1])
def segfunc(x, y):
return min(x, y)
def gindex(self, l, r):
l += self.num
r += self.num
lm = l >> (l & -l).bit_length()
rm = r >> (r & -r).bit_length()
while r > l:
if l <= lm:
yield l
if r <= rm:
yield r
r >>= 1
l >>= 1
while l:
yield l
l >>= 1
def propagates(self, *ids):
for i in reversed(ids):
v = self.lazy[i]
if v is None:
continue
self.lazy[i] = None
self.lazy[2*i] = v
self.lazy[2*i+1] = v
self.tree[2*i] = v
self.tree[2*i+1] = v
def update(self, l, r, x):
ids = self.gindex(l, r)
self.propagates(*self.gindex(l, r))
l += self.num
r += self.num
while l < r:
if l & 1:
self.lazy[l] = x
self.tree[l] = x
l += 1
if r & 1:
self.lazy[r-1] = x
self.tree[r-1] = x
r >>= 1
l >>= 1
for i in ids:
self.tree[i] = self.segfunc(self.tree[2*i], self.tree[2*i+1])
def query(self, l, r):
ids = self.gindex(l, r)
self.propagates(*self.gindex(l, r))
res = self.ide_ele
l += self.num
r += self.num
while l < r:
if l & 1:
res = self.segfunc(res, self.tree[l])
l += 1
if r & 1:
res = self.segfunc(res, self.tree[r-1])
l >>= 1
r >>= 1
return res
T = TypeVar('T')
class SortedSet(Generic[T]):
BUCKET_RATIO = 50
REBUILD_RATIO = 170
def _build(self, a=None) -> None:
"Evenly divide `a` into buckets."
if a is None:
a = list(self)
size = self.size = len(a)
bucket_size = int(math.ceil(math.sqrt(size / self.BUCKET_RATIO)))
self.a = [a[size * i // bucket_size: size * (i + 1) // bucket_size] for i in range(bucket_size)]
def __init__(self, a: Iterable[T] = []) -> None:
"Make a new SortedSet from iterable. / O(N) if sorted and unique / O(N log N)"
a = list(a)
if not all(a[i] < a[i + 1] for i in range(len(a) - 1)):
a = sorted(set(a))
self._build(a)
def __iter__(self) -> Iterator[T]:
for i in self.a:
for j in i:
yield j
def __reversed__(self) -> Iterator[T]:
for i in reversed(self.a):
for j in reversed(i):
yield j
def __len__(self) -> int:
return self.size
def __repr__(self) -> str:
return "SortedSet" + str(self.a)
def __str__(self) -> str:
s = str(list(self))
return "{" + s[1: len(s) - 1] + "}"
def _find_bucket(self, x: T) -> List[T]:
"Find the bucket which should contain x. self must not be empty."
for a in self.a:
if x <= a[-1]:
return a
return a
def __contains__(self, x: T) -> bool:
if self.size == 0:
return False
a = self._find_bucket(x)
i = bisect_left(a, x)
return i != len(a) and a[i] == x
def add(self, x: T) -> bool:
"Add an element and return True if added. / O(√N)"
if self.size == 0:
self.a = [[x]]
self.size = 1
return True
a = self._find_bucket(x)
i = bisect_left(a, x)
if i != len(a) and a[i] == x:
return False
a.insert(i, x)
self.size += 1
if len(a) > len(self.a) * self.REBUILD_RATIO:
self._build()
return True
def discard(self, x: T) -> bool:
"Remove an element and return True if removed. / O(√N)"
if self.size == 0:
return False
a = self._find_bucket(x)
i = bisect_left(a, x)
if i == len(a) or a[i] != x:
return False
a.pop(i)
self.size -= 1
if len(a) == 0:
self._build()
return True
def lt(self, x: T) -> Optional[T]:
"Find the largest element < x, or None if it doesn't exist."
for a in reversed(self.a):
if a[0] < x:
return a[bisect_left(a, x) - 1]
def le(self, x: T) -> Optional[T]:
"Find the largest element <= x, or None if it doesn't exist."
for a in reversed(self.a):
if a[0] <= x:
return a[bisect_right(a, x) - 1]
def gt(self, x: T) -> Optional[T]:
"Find the smallest element > x, or None if it doesn't exist."
for a in self.a:
if a[-1] > x:
return a[bisect_right(a, x)]
def ge(self, x: T) -> Optional[T]:
"Find the smallest element >= x, or None if it doesn't exist."
for a in self.a:
if a[-1] >= x:
return a[bisect_left(a, x)]
def __getitem__(self, x: int) -> T:
"Return the x-th element, or IndexError if it doesn't exist."
if x < 0:
x += self.size
if x < 0:
raise IndexError
for a in self.a:
if x < len(a):
return a[x]
x -= len(a)
raise IndexError
def index(self, x: T) -> int:
"Count the number of elements < x."
ans = 0
for a in self.a:
if a[-1] >= x:
return ans + bisect_left(a, x)
ans += len(a)
return ans
def index_right(self, x: T) -> int:
"Count the number of elements <= x."
ans = 0
for a in self.a:
if a[-1] > x:
return ans + bisect_right(a, x)
ans += len(a)
return ans
class SortedMultiset(Generic[T]):
BUCKET_RATIO = 50
REBUILD_RATIO = 170
def _build(self, a=None) -> None:
"Evenly divide `a` into buckets."
if a is None:
a = list(self)
size = self.size = len(a)
bucket_size = int(math.ceil(math.sqrt(size / self.BUCKET_RATIO)))
self.a = [a[size * i // bucket_size: size * (i + 1) // bucket_size] for i in range(bucket_size)]
def __init__(self, a: Iterable[T] = []) -> None:
"Make a new SortedMultiset from iterable. / O(N) if sorted / O(N log N)"
a = list(a)
if not all(a[i] <= a[i + 1] for i in range(len(a) - 1)):
a = sorted(a)
self._build(a)
def __iter__(self) -> Iterator[T]:
for i in self.a:
for j in i:
yield j
def __reversed__(self) -> Iterator[T]:
for i in reversed(self.a):
for j in reversed(i):
yield j
def __len__(self) -> int:
return self.size
def __repr__(self) -> str:
return "SortedMultiset" + str(self.a)
def __str__(self) -> str:
s = str(list(self))
return "{" + s[1: len(s) - 1] + "}"
def _find_bucket(self, x: T) -> List[T]:
"Find the bucket which should contain x. self must not be empty."
for a in self.a:
if x <= a[-1]:
return a
return a
def __contains__(self, x: T) -> bool:
if self.size == 0:
return False
a = self._find_bucket(x)
i = bisect_left(a, x)
return i != len(a) and a[i] == x
def count(self, x: T) -> int:
"Count the number of x."
return self.index_right(x) - self.index(x)
def add(self, x: T) -> None:
"Add an element. / O(√N)"
if self.size == 0:
self.a = [[x]]
self.size = 1
return
a = self._find_bucket(x)
insort(a, x)
self.size += 1
if len(a) > len(self.a) * self.REBUILD_RATIO:
self._build()
def discard(self, x: T) -> bool:
"Remove an element and return True if removed. / O(√N)"
if self.size == 0:
return False
a = self._find_bucket(x)
i = bisect_left(a, x)
if i == len(a) or a[i] != x:
return False
a.pop(i)
self.size -= 1
if len(a) == 0:
self._build()
return True
def lt(self, x: T) -> Optional[T]:
"Find the largest element < x, or None if it doesn't exist."
for a in reversed(self.a):
if a[0] < x:
return a[bisect_left(a, x) - 1]
def le(self, x: T) -> Optional[T]:
"Find the largest element <= x, or None if it doesn't exist."
for a in reversed(self.a):
if a[0] <= x:
return a[bisect_right(a, x) - 1]
def gt(self, x: T) -> Optional[T]:
"Find the smallest element > x, or None if it doesn't exist."
for a in self.a:
if a[-1] > x:
return a[bisect_right(a, x)]
def ge(self, x: T) -> Optional[T]:
"Find the smallest element >= x, or None if it doesn't exist."
for a in self.a:
if a[-1] >= x:
return a[bisect_left(a, x)]
def __getitem__(self, x: int) -> T:
"Return the x-th element, or IndexError if it doesn't exist."
if x < 0:
x += self.size
if x < 0:
raise IndexError
for a in self.a:
if x < len(a):
return a[x]
x -= len(a)
raise IndexError
def index(self, x: T) -> int:
"Count the number of elements < x."
ans = 0
for a in self.a:
if a[-1] >= x:
return ans + bisect_left(a, x)
ans += len(a)
return ans
def index_right(self, x: T) -> int:
"Count the number of elements <= x."
ans = 0
for a in self.a:
if a[-1] > x:
return ans + bisect_right(a, x)
ans += len(a)
return ans
# 配列の転倒数を求める（o(NlogN)）
def inversion_num(L: list):
max_N = max(L)
bit = BIT(max_N)
cnt = 0
for i, l in enumerate(L):
cnt += i-bit.sum(l)
bit.add(l, 1)
return cnt
# 約数列挙
def make_divisors(n):
lower_divisors, upper_divisors = [], []
i = 1
while i*i <= n:
if n % i == 0:
lower_divisors.append(i)
if i != n // i:
upper_divisors.append(n//i)
i += 1
return lower_divisors + upper_divisors[::-1]
# Nまでの素数列挙
# 計算量 O(logN)
def prime_list(N):
H = [False] * (N + 1)
primes = []
for i in range(2, N + 1):
if H[i]:
continue
primes.append(i)
for j in range(i, N + 1, i):
H[j] = True
return primes
class ModInt:
def __init__(self, x, mod=998244353):
self.x = x % mod
self.mod = mod
def __str__(self):
return str(self.x)
__repr__ = __str__
def __add__(self, other):
return (
ModInt(self.x + other.x) if isinstance(other, ModInt) else
ModInt(self.x + other)
)
def __sub__(self, other):
return (
ModInt(self.x - other.x) if isinstance(other, ModInt) else
ModInt(self.x - other)
)
def __mul__(self, other):
return (
ModInt(self.x*other.x) if isinstance(other, ModInt) else
ModInt(self.x*other)
)
def __truediv__(self, other):
return (
ModInt(
self.x*pow(other.x, self.mod-2, self.mod)
) if isinstance(other, ModInt) else
ModInt(self.x*pow(other, self.mod-2, self.mod))
)
def __pow__(self, other):
return (
ModInt(pow(self.x, other.x, self.mod)) if isinstance(other, ModInt) else
ModInt(pow(self.x, other, self.mod))
)
__radd__ = __add__
def __rsub__(self, other):
return (
ModInt(other.x-self.x) if isinstance(other, ModInt) else
ModInt(other-self.x)
)
__rmul__ = __mul__
def __rtruediv__(self, other):
return (
ModInt(
other.x * pow(self.x, self.mod-2, self.mod)
) if isinstance(other, ModInt) else
ModInt(other * pow(self.x, self.mod-2, self.mod))
)
def __rpow__(self, other):
return (
ModInt(pow(other.x, self.x, self.mod)) if isinstance(other, ModInt) else
ModInt(pow(other, self.x, self.mod))
)
class FFT():
def primitive_root_constexpr(self, m):
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 = [0]*20
divs[0] = 2
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 (1):
ok = True
for i in range(cnt):
if pow(g, (m-1)//divs[i], m) == 1:
ok = False
break
if ok:
return g
g += 1
def bsf(self, x):
res = 0
while (x % 2 == 0):
res += 1
x //= 2
return res
rank2 = 0
root = []
iroot = []
rate2 = []
irate2 = []
rate3 = []
irate3 = []
def __init__(self, MOD):
self.mod = MOD
self.g = self.primitive_root_constexpr(self.mod)
self.rank2 = self.bsf(self.mod-1)
self.root = [0 for i in range(self.rank2+1)]
self.iroot = [0 for i in range(self.rank2+1)]
self.rate2 = [0 for i in range(self.rank2)]
self.irate2 = [0 for i in range(self.rank2)]
self.rate3 = [0 for i in range(self.rank2-1)]
self.irate3 = [0 for i in range(self.rank2-1)]
self.root[self.rank2] = pow(self.g, (self.mod-1) >> self.rank2, self.mod)
self.iroot[self.rank2] = pow(self.root[self.rank2], self.mod-2, self.mod)
for i in range(self.rank2-1, -1, -1):
self.root[i] = (self.root[i+1]**2) % self.mod
self.iroot[i] = (self.iroot[i+1]**2) % self.mod
prod = 1
iprod = 1
for i in range(self.rank2-1):
self.rate2[i] = (self.root[i+2]*prod) % self.mod
self.irate2[i] = (self.iroot[i+2]*iprod) % self.mod
prod = (prod*self.iroot[i+2]) % self.mod
iprod = (iprod*self.root[i+2]) % self.mod
prod = 1
iprod = 1
for i in range(self.rank2-2):
self.rate3[i] = (self.root[i+3]*prod) % self.mod
self.irate3[i] = (self.iroot[i+3]*iprod) % self.mod
prod = (prod*self.iroot[i+3]) % self.mod
iprod = (iprod*self.root[i+3]) % self.mod
def butterfly(self, a):
n = len(a)
h = (n-1).bit_length()
LEN = 0
while (LEN < h):
if (h-LEN == 1):
p = 1 << (h-LEN-1)
rot = 1
for s in range(1 << LEN):
offset = s << (h-LEN)
for i in range(p):
l = a[i+offset]
r = a[i+offset+p]*rot
a[i+offset] = (l+r) % self.mod
a[i+offset+p] = (l-r) % self.mod
rot *= self.rate2[(~s & -~s).bit_length()-1]
rot %= self.mod
LEN += 1
else:
p = 1 << (h-LEN-2)
rot = 1
imag = self.root[2]
for s in range(1 << LEN):
rot2 = (rot*rot) % self.mod
rot3 = (rot2*rot) % self.mod
offset = s << (h-LEN)
for i in range(p):
a0 = a[i+offset]
a1 = a[i+offset+p]*rot
a2 = a[i+offset+2*p]*rot2
a3 = a[i+offset+3*p]*rot3
a1na3imag = (a1-a3) % self.mod*imag
a[i+offset] = (a0+a2+a1+a3) % self.mod
a[i+offset+p] = (a0+a2-a1-a3) % self.mod
a[i+offset+2*p] = (a0-a2+a1na3imag) % self.mod
a[i+offset+3*p] = (a0-a2-a1na3imag) % self.mod
rot *= self.rate3[(~s & -~s).bit_length()-1]
rot %= self.mod
LEN += 2
def butterfly_inv(self, a):
n = len(a)
h = (n-1).bit_length()
LEN = h
while (LEN):
if (LEN == 1):
p = 1 << (h-LEN)
irot = 1
for s in range(1 << (LEN-1)):
offset = s << (h-LEN+1)
for i in range(p):
l = a[i+offset]
r = a[i+offset+p]
a[i+offset] = (l+r) % self.mod
a[i+offset+p] = (l-r)*irot % self.mod
irot *= self.irate2[(~s & -~s).bit_length()-1]
irot %= self.mod
LEN -= 1
else:
p = 1 << (h-LEN)
irot = 1
iimag = self.iroot[2]
for s in range(1 << (LEN-2)):
irot2 = (irot*irot) % self.mod
irot3 = (irot*irot2) % self.mod
offset = s << (h-LEN+2)
for i in range(p):
a0 = a[i+offset]
a1 = a[i+offset+p]
a2 = a[i+offset+2*p]
a3 = a[i+offset+3*p]
a2na3iimag = (a2-a3)*iimag % self.mod
a[i+offset] = (a0+a1+a2+a3) % self.mod
a[i+offset+p] = (a0-a1+a2na3iimag)*irot % self.mod
a[i+offset+2*p] = (a0+a1-a2-a3)*irot2 % self.mod
a[i+offset+3*p] = (a0-a1-a2na3iimag)*irot3 % self.mod
irot *= self.irate3[(~s & -~s).bit_length()-1]
irot %= self.mod
LEN -= 2
def convolution(self, a, b):
n = len(a)
m = len(b)
if not (a) or not (b):
return []
if min(n, m) <= 40:
res = [0]*(n+m-1)
for i in range(n):
for j in range(m):
res[i+j] += a[i]*b[j]
res[i+j] %= self.mod
return res
z = 1 << ((n+m-2).bit_length())
a = a+[0]*(z-n)
b = b+[0]*(z-m)
self.butterfly(a)
self.butterfly(b)
c = [(a[i]*b[i]) % self.mod for i in range(z)]
self.butterfly_inv(c)
iz = pow(z, self.mod-2, self.mod)
for i in range(n+m-1):
c[i] = (c[i]*iz) % self.mod
return c[:n+m-1]
class mf_graph:
n = 1
g = [[] for i in range(1)]
pos = []
def __init__(self, N):
self.n = N
self.g = [[] for i in range(N)]
self.pos = []
def add_edge(self, From, To, cap):
assert 0 <= From and From < self.n
assert 0 <= To and To < self.n
assert 0 <= cap
m = len(self.pos)
from_id = len(self.g[From])
self.pos.append([From, from_id])
to_id = len(self.g[To])
if From == To:
to_id += 1
self.g[From].append([To, to_id, cap])
self.g[To].append([From, from_id, 0])
return m
def get_edge(self, i):
m = len(self.pos)
assert 0 <= i and i < m
_e = self.g[self.pos[i][0]][self.pos[i][1]]
_re = self.g[_e[0]][_e[1]]
return [self.pos[i][0], _e[0], _e[2]+_re[2], _re[2]]
def edges(self):
m = len(self.pos)
result = []
for i in range(m):
a, b, c, d = self.get_edge(i)
result.append({"from": a, "to": b, "cap": c, "flow": d})
return result
def change_edge(self, i, new_cap, new_flow):
m = len(self.pos)
assert 0 <= i and i < m
assert 0 <= new_flow and new_flow <= new_cap
_e = self.g[self.pos[i][0]][self.pos[i][1]]
_re = self.g[_e[0]][_e[1]]
_e[2] = new_cap-new_flow
_re[2] = new_flow
def flow(self, s, t, flow_limit=(1 << 63)-1):
assert 0 <= s and s < self.n
assert 0 <= t and t < self.n
assert s != t
def bfs():
level = [-1 for i in range(self.n)]
level[s] = 0
que = collections.deque([])
que.append(s)
while (que):
v = que.popleft()
for to, rev, cap in self.g[v]:
if cap == 0 or level[to] >= 0:
continue
level[to] = level[v]+1
if to == t:
return level
que.append(to)
return level
def dfs(v, up):
if (v == s):
return up
res = 0
level_v = level[v]
for i in range(Iter[v], len(self.g[v])):
Iter[v] = i
to, rev, cap = self.g[v][i]
if (level_v <= level[to] or self.g[to][rev][2] == 0):
continue
d = dfs(to, min(up-res, self.g[to][rev][2]))
if d <= 0:
continue
self.g[v][i][2] += d
self.g[to][rev][2] -= d
res += d
if res == up:
return res
level[v] = self.n
return res
flow = 0
while (flow < flow_limit):
level = bfs()
if level[t] == -1:
break
Iter = [0 for i in range(self.n)]
f = dfs(t, flow_limit-flow)
if not (f):
break
flow += f
return flow
def min_cut(self, s):
visited = [False for i in range(self.n)]
que = collections.deque([])
que.append(s)
while (len(que) > 0):
p = que.popleft()
visited[p] = True
for to, rev, cap in self.g[p]:
if cap and not (visited[to]):
visited[to] = True
que.append(to)
return visited
def main():
N = I()
A,B,C=MI()
s=[(A,3),(B,5),(C,10)]
dp=[0]*(N+1)
for i in range(N):
for j in range(3):
if i+s[j][1]<=N:
dp[i+s[j][1]]=max(dp[i+s[j][1]],dp[i]+s[j][0])
print(dp[N])
if __name__ == "__main__":
main()