Problem p02737 (python)

Fixed submission:
from collections import defaultdict

M = 998244353
B = 10**18 % M

def mex(s):
  for i in range(max(s)+2):
    if i not in s:
      return i

def ext_euc(a, b):
  x1, y1, z1 = 1, 0, a
  x2, y2, z2 = 0, 1, b
  while z1 != 1:
    d, m = divmod(z2,z1)
    x1, x2 = x2-d*x1, x1
    y1, y2 = y2-d*y1, y1
    z1, z2 = m, z1
  return x1, y1

def inv_mod(a, b, m):
  x, y = ext_euc(a, m)
  return (x * b % m)

def calc_grundy(e):
  g = {}
  sum_g = defaultdict(int)
  sum_g[0] = inv_mod(B-1, pow(B, N+1, M)-B, M)
  for i in sorted(e.keys(), reverse=True):
    m = mex({g.get(j,0) for j in e[i]})
    if m:
      g[i] = m
      x = pow(B, i, M)
      sum_g[m] += x
      sum_g[0] -= x
  return sum_g

def get_edge():
  M = int(input())
  e = defaultdict(set)
  for i in range(M):
    a, b = sorted(map(int, input().split()))
    e[a].add(b)
  return e

def solve(N, edge):
  sum_g = list(map(calc_grundy, edge))
  ret = 0
  for gx, x in sum_g[0].items():
    for gy, y in sum_g[1].items():
      gz = gx^gy
      z = sum_g[2][gz]
      ret = (ret + x*y*z)%M
  return ret

N = int(input())
edge = [get_edge() for i in range(3)]

print(solve(N, edge))

Buggy submission (verdict: Runtime Error):
from collections import defaultdict
import sys

input = lambda: sys.stdin.readline().rstrip()

M = 998244353
B = pow(10, 18, M)
N = int(input())

def ext_euc(a, b):
  x1, y1, z1 = 1, 0, a
  x2, y2, z2 = 0, 1, b
  while z1 != 1:
    d, m = divmod(z2,z1)
    x1, x2 = x2-d*x1, x1
    y1, y2 = y2-d*y1, y1
    z1, z2 = m, z1
  return x1, y1

def inv_mod(a, b, m):
  x, y = ext_euc(a, m)
  return (x * b % m)

def mex(s):
  for i in range(N+1):
    if i not in s:
      return i

def calc_grundy(e):
  g = {}
  sum_g = defaultdict(int)
  sum_g[0] = inv_mod(B-1, pow(B, N+1, M)-B, M)
  for i in range(N, 0, -1):
    if i not in e:
      continue
    m = mex({g.get(j, 0) for j in e[i]})
    if m:
      g[i] = m
  prev_i = 1
  prev_W = B
  for i in range(1, N+1):
    if i in g:
      W = (W * pow(B, i-prev_i, M)) % M
      sum_g[g[i]] = (sum_g[g[i]] + W) % M
      sum_g[0]  = (sum_g[0] - W) % M
      prev_i, prev_W = i, W
  
  return sum_g

def read_edge():
  M = int(input())
  e = defaultdict(list)
  for i in range(M):
    a, b = sorted(map(int, input().split()))
    e[a].append(b)
  return e

def solve(N, edge):
  sum_g = list(map(calc_grundy, edge))
  ret = 0
  for gx, sx in sum_g[0].items():
    for gy, sy in sum_g[1].items():
      gz = gx^gy
      sz = sum_g[2][gz]
      if sz:
        ret = (ret + sx*sy*sz) % M
  return ret

edge = [read_edge() for i in range(3)]

print(solve(N, edge))

Buggy submission (verdict: Runtime Error):
from collections import defaultdict
import sys

input = lambda: sys.stdin.readline().rstrip()

M = 998244353
B = pow(10, 18, M)
N = int(input())

def ext_euc(a, b):
  x1, y1, z1 = 1, 0, a
  x2, y2, z2 = 0, 1, b
  while z1 != 1:
    d, m = divmod(z2,z1)
    x1, x2 = x2-d*x1, x1
    y1, y2 = y2-d*y1, y1
    z1, z2 = m, z1
  return x1, y1

def inv_mod(a, b, m):
  x, y = ext_euc(a, m)
  return (x * b % m)

def mex(s):
  for i in range(N+1):
    if i not in s:
      return i

def calc_grundy(e):
  g = {}
  sum_g = defaultdict(int)
  sum_g[0] = inv_mod(B-1, pow(B, N+1, M)-B, M)
  for i in range(N, 0, -1):
    if i not in e:
      continue
    m = mex({g.get(j, 0) for j in e[i]})
    if m:
      g[i] = m
  prev_i = 1
  prev_W = B
  for i in range(1, N+1):
    if i in g:
      W = (B * pow(B, prev_i-i, M)) % M
      sum_g[g[i]] = (sum_g[g[i]] + W) % M
      sum_g[0]  = (sum_g[0] - W) % M
      prev_i, prev_W = i, W
  
  return sum_g

def read_edge():
  M = int(input())
  e = defaultdict(list)
  for i in range(M):
    a, b = sorted(map(int, input().split()))
    e[a].append(b)
  return e

def solve(N, edge):
  sum_g = list(map(calc_grundy, edge))
  ret = 0
  for gx, sx in sum_g[0].items():
    for gy, sy in sum_g[1].items():
      gz = gx^gy
      sz = sum_g[2][gz]
      if sz:
        ret = (ret + sx*sy*sz) % M
  return ret

edge = [read_edge() for i in range(3)]

print(solve(N, edge))

Buggy submission (verdict: Runtime Error):
from collections import defaultdict
import sys
input = lambda: sys.stdin.readline().rstrip()

M = 998244353
B = pow(10, 18, M)
N = int(input())

def geometric_mod(a, r, m, n):
  x = a
  for i in range(n):
    yield x
    x = (x*r)%m

BB = list(geometric_mod(1, B, M, N+2))

def ext_euc(a, b):
  x1, y1, z1 = 1, 0, a
  x2, y2, z2 = 0, 1, b
  while z1 != 1:
    d, m = divmod(z2,z1)
    x1, x2 = x2-d*x1, x1
    y1, y2 = y2-d*y1, y1
    z1, z2 = m, z1
  return x1, y1

def inv_mod(a, b, m):
  x, y = ext_euc(a, m)
  return (x * b % m)

def mex(s):
  for i in range(N+1):
    if i not in s:
      return i

def calc_grundy(e):
  g = {}
  sum_g = defaultdict(int)
  sum_g[0] = inv_mod(B-1, pow(B, N+1, M)-B, M)
  for i in range(N, 0, -1):
    if i not in e:
      continue
    m = mex({g.get(j, 0) for j in e[i]})
    if m:
      g[i] = m
      sum_g[g[i]] = (sum_g[g[i]] + BB[i]) % M
      sum_g[0]  = (sum_g[0] - BB[i]) % M

  return sum_g

def read_edge():
  M = int(input())
  e = defaultdict(list)
  for i in range(M):
    a, b = sorted(map(int, input().split()))
    e[a].add(b)
  return e

def solve(N, edge):
  sum_g = list(map(calc_grundy, edge))
  ret = 0
  for gx, sx in sum_g[0].items():
    for gy, sy in sum_g[1].items():
      gz = gx^gy
      sz = sum_g[2][gz]
      if sz:
        ret = (ret + sx*sy*sz) % M
  return ret


edge = [read_edge() for i in range(3)]

print(solve(N, edge))

Buggy submission (verdict: Runtime Error):
from collections import defaultdict

M = 998244353
B = pow(10, 18, M)
N = int(input())

def geometric_mod(a, r, m, n):
  x = a
  for i in range(n):
    yield x
    x = (x*r)%m

BB = list(geometric_mod(1, B, M, N+2))

def ext_euc(a, b):
  x1, y1, z1 = 1, 0, a
  x2, y2, z2 = 0, 1, b
  while z1 != 1:
    d, m = divmod(z2,z1)
    x1, x2 = x2-d*x1, x1
    y1, y2 = y2-d*y1, y1
    z1, z2 = m, z1
  return x1, y1

def inv_mod(a, b, m):
  x, y = ext_euc(a, m)
  return (x * b % m)

def mex(s):
  for i in range(N+1):
    if i not in s:
      return i

def calc_grundy(e):
  e = set(e)
  g = {}
  sum_g = defaultdict(int)
  sum_g[0] = inv_mod(B-1, pow(B, N+1, M)-B, M)
  for i in range(N, 0, -1):
    if i not in e:
      continue
    m = mex({g.get(j, 0) for j in e[i]})
    if m:
      g[i] = m
      sum_g[g[i]] = (sum_g[g[i]] + BB[i]) % M
      sum_g[0]  = (sum_g[0] - BB[i]) % M

  return sum_g

def read_edge():
  M = int(input())
  e = defaultdict(list)
  for i in range(M):
    a, b = sorted(map(int, input().split()))
    e[a].append(b)
  return e

def solve(N, edge):
  sum_g = list(map(calc_grundy, edge))
  ret = 0
  for gx, sx in sum_g[0].items():
    for gy, sy in sum_g[1].items():
      gz = gx^gy
      sz = sum_g[2][gz]
      if sz:
        ret = (ret + sx*sy*sz) % M
  return ret


edge = [read_edge() for i in range(3)]

print(solve(N, edge))

Buggy submission (verdict: Runtime Error):
from collections import defaultdict

M = 998244353
B = pow(10, 18, M)
N = int(input())

def ext_euc(a, b):
  x1, y1, z1 = 1, 0, a
  x2, y2, z2 = 0, 1, b
  while z1 != 1:
    d, m = divmod(z2,z1)
    x1, x2 = x2-d*x1, x1
    y1, y2 = y2-d*y1, y1
    z1, z2 = m, z1
  return x1, y1

def inv_mod(a, b, m):
  x, y = ext_euc(a, m)
  return (x * b % m)

def mex(s):
  for i in range(N+1):
    if i not in s:
      return i

def calc_grundy(e):
  g = {}
  sum_g = defaultdict(int)
  sum_g[0] = inv_mod(B-1, pow(B, N+1, M)-B, M)
  for i in range(N, 0, -1):
    if i not in e:
      continue
    m = mex({g.get(j, 0) for j in e[i]})
    if m:
      g[i] = m
  x = 1
  for i in range(1, N+1):
    x = (x * B) % M
    if g[i]:
      sum_g[g[i]] += x
      sum_g[0] -= x
  return sum_g

def read_edge():
  M = int(input())
  e = defaultdict(set)
  for i in range(M):
    a, b = sorted(map(int, input().split()))
    e[a].add(b)
  return e

def solve(N, edge):
  sum_g = list(map(calc_grundy, edge))
  ret = 0
  for gx, sx in sum_g[0].items():
    for gy, sy in sum_g[1].items():
      gz = gx^gy
      sz = sum_g[2][gz]
      if sz:
        ret += (sx*sy*sz) % M
  return ret%M


edge = [read_edge() for i in range(3)]

print(solve(N, edge))

Buggy submission (verdict: Runtime Error):
from collections import defaultdict

M = 998244353
B = pow(10, 18, M)
N = int(input())

def ext_euc(a, b):
  x1, y1, z1 = 1, 0, a
  x2, y2, z2 = 0, 1, b
  while z1 != 1:
    d, m = divmod(z2,z1)
    x1, x2 = x2-d*x1, x1
    y1, y2 = y2-d*y1, y1
    z1, z2 = m, z1
  return x1, y1

def inv_mod(a, b, m):
  x, y = ext_euc(a, m)
  return (x * b % m)

def mex(s):
  for i in range(N+1):
    if i not in s:
      return i

def calc_grundy(e):
  g = {}
  sum_g = defaultdict(int)
  sum_g[0] = inv_mod(B-1, pow(B, N+1, M)-B, M)
  for i in range(N, 0, -1):
    if i not in e:
      continue
    m = mex({g.get(j, 0) for j in e[i]})
    if m:
      g[i] = m
  x = 1
  for i in range(1, N+1)
    x = (x * B) % M
    if g[i]:
      sum_g[g[i]] += x
      sum_g[0] -= x
  return sum_g

def read_edge():
  M = int(input())
  e = defaultdict(set)
  for i in range(M):
    a, b = sorted(map(int, input().split()))
    e[a].add(b)
  return e

def solve(N, edge):
  sum_g = list(map(calc_grundy, edge))
  ret = 0
  for gx, sx in sum_g[0].items():
    for gy, sy in sum_g[1].items():
      gz = gx^gy
      sz = sum_g[2][gz]
      if sz:
        ret += (sx*sy*sz) % M
  return ret%M


edge = [read_edge() for i in range(3)]

print(solve(N, edge))