Problem:
 Score : 900 points    Problem Statement Given are simple undirected graphs X , Y , Z , with N vertices each and M_1 , M_2 , M_3 edges, respectively.
The vertices in X , Y , Z are respectively called x_1, x_2, \dots, x_N , y_1, y_2, \dots, y_N , z_1, z_2, \dots, z_N .
The edges in X , Y , Z are respectively (x_{a_i}, x_{b_i}) , (y_{c_i}, y_{d_i}) , (z_{e_i}, z_{f_i}) .  Based on X , Y , Z , we will build another undirected graph W with N^3 vertices.
There are N^3 ways to choose a vertex from each of the graphs X , Y , Z . Each of these choices corresponds to the vertices in W one-to-one. Let (x_i, y_j, z_k) denote the vertex in W corresponding to the choice of x_i, y_j, z_k .  We will span edges in W as follows:   For each edge (x_u, x_v) in X and each w, l , span an edge between (x_u, y_w, z_l) and (x_v, y_w, z_l) .  For each edge (y_u, y_v) in Y and each w, l , span an edge between (x_w, y_u, z_l) and (x_w, y_v, z_l) .  For each edge (z_u, z_v) in Z and each w, l , span an edge between (x_w, y_l, z_u) and (x_w, y_l, z_v) .   Then, let the weight of the vertex (x_i, y_j, z_k) in W be 1,000,000,000,000,000,000^{(i +j + k)} = 10^{18(i + j + k)} . Find the maximum possible total weight of the vertices in an independent set in W , and print that total weight modulo 998,244,353 .      Constraints  2 \leq N \leq 100,000  1 \leq M_1, M_2, M_3 \leq 100,000  1 \leq a_i, b_i, c_i, d_i, e_i, f_i \leq N  X , Y , and Z are simple, that is, they have no self-loops and no multiple edges.         Input Input is given from Standard Input in the following format:  N  M_1  a_1  b_1  a_2  b_2  \vdots  a_{M_1}  b_{M_1}  M_2  c_1  d_1  c_2  d_2  \vdots  c_{M_2}  d_{M_2}  M_3  e_1  f_1  e_2  f_2  \vdots  e_{M_3}  f_{M_3}       Output Print the maximum possible total weight of an independent set in W , modulo 998,244,353 .        Sample Input 1 2
1
1 2
1
1 2
1
1 2      Sample Output 1 46494701  The maximum possible total weight of an independent set is that of the set (x_2, y_1, z_1) , (x_1, y_2, z_1) , (x_1, y_1, z_2) , (x_2, y_2, z_2) . The output should be (3 \times 10^{72} + 10^{108}) modulo 998,244,353 , which is 46,494,701 .       Sample Input 2 3
3
1 3
1 2
3 2
2
2 1
2 3
1
2 1      Sample Output 2 883188316       Sample Input 3 100000
1
1 2
1
99999 100000
1
1 100000      Sample Output 3 318525248

Solution (Python):
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].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))

Solution (Python):
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(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 = (ret + sx*sy*sz) % M
  return ret


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

print(solve(N, edge))

Solution (Python):
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)
  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
  sum_g[0] = (inv_mod(B-1, pow(B, N+1, M)-B, M) - sum_g[0]) % M
  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 = (ret + sx*sy*sz) % M
  return ret


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

print(solve(N, edge))

Solution (Python):
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)
  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
  sum_g[0] = (inv_mod(B-1, pow(B, N+1, M)-B, M) - sum_g[0]) % M
  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 = (ret + sx*sy*sz) % M
  return ret


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

print(solve(N, edge))

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

Solution (Python):
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 set(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))

Solution (Python):
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 set(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))

Solution (Python):
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):
  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 set(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))

Solution (Python):
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):
  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(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 = (ret + sx*sy*sz) % M
  return ret


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

print(solve(N, edge))

Solution (Python):
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 = {}
  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 = defaultdict(int)
  sum_g[0] = inv_mod(B-1, pow(B, N+1, M)-B, M)
  x = 1
  for i in range(1, N+1):
    x = (x * B) % M
    if i in g:
      sum_g[g[i]] = (sum_g[g[i]] + x) % M
      sum_g[0]  = (sum_g[0] - x) % M
  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 = (ret + sx*sy*sz) % M
  return ret


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

print(solve(N, edge))

Solution (Python):
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 = {}
  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 = defaultdict(int)
  sum_g[0] = inv_mod(B-1, pow(B, N+1, M)-B, M)
  x = 1
  for i in range(1, N+1):
    x = (x * B) % M
    if i in g:
      j = g.pop(i)
      sum_g[j] = (sum_g[j] + x) % M
      sum_g[0]  = (sum_g[0] - x) % M
      if not g:
        break
  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))

Solution (Python):
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 = {}
  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 = defaultdict(int)
  sum_g[0] = inv_mod(B-1, pow(B, N+1, M)-B, M)
  x = 1
  for i in range(1, N+1):
    x = (x * B) % M
    if i in g:
      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))

Solution (Python):
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 = pow(B, i, M)
      sum_g[m] += 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))

Solution (Python):
from collections import defaultdict

M = 998244353
B = pow(10, 18, M)

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 = pow(B, i, M)
      sum_g[m] = (sum_g[m] + x) % M
      sum_g[0] = (sum_g[0] - x) % M
  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 = (ret + sx*sy*sz)%M
  return ret

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

print(solve(N, edge))

Solution (Python):
from collections import defaultdict

M = 998244353
B = 10**18 % M

def mex(s):
  for i in range(N+1):
    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 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 = (ret + sx*sy*sz)%M
  return ret

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

print(solve(N, edge))

Solution (Python):
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 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 = (ret + sx*sy*sz)%M
  return ret

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

print(solve(N, edge))

Solution (Python):
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))

Solution (Python):
import sys
input = lambda: sys.stdin.readline().rstrip()

def calc():
    def mex(i):
        D = {}
        for j in X[i]:
            D[G[j]] = 1
        for g in range(N + 1):
            if g not in D:
                return g
    M = int(input())
    X = [[] for _ in range(N)]
    for _ in range(M):
        a, b = map(int, input().split())
        X[N - min(a, b)].append(N - max(a, b))
    G = [0] * N
    for i in range(N):
        G[i] = mex(i)
    H = [0] * 1024
    a = 1
    for i in range(N)[::-1]:
        a = a * A % P
        H[G[i]] = (H[G[i]] + a) % P
    return H

P = 998244353
A = pow(10, 18, P)
N = int(input())
H1, H2, H3 = calc(), calc(), calc()
ans = 0
for i in range(1024):
    if H1[i] == 0: continue
    for j in range(1024):
        if H2[j] == 0: continue
        ans = (ans + H1[i] * H2[j] * H3[i^j]) % P

print(ans)

Solution (Python):
import sys
input = lambda: sys.stdin.readline().rstrip()

def calc():
    def mex(i):
        t = 0
        for j in X[i]:
            t |= 1 << G[j]
        t = ~t
        return (t & -t).bit_length() - 1
    M = int(input())
    X = [[] for _ in range(N)]
    for _ in range(M):
        a, b = map(int, input().split())
        X[N - min(a, b)].append(N - max(a, b))
    G = [0] * N
    for i in range(N):
        G[i] = mex(i)
    H = [0] * 1024
    a = 1
    for i in range(N)[::-1]:
        a = a * A % P
        H[G[i]] = (H[G[i]] + a) % P
    return H

P = 998244353
A = pow(10, 18, P)
N = int(input())
H1, H2, H3 = calc(), calc(), calc()
ans = 0
for i in range(1024):
    if H1[i] == 0: continue
    for j in range(1024):
        if H2[j] == 0: continue
        ans = (ans + H1[i] * H2[j] * H3[i^j]) % P

print(ans)

Solution (Python):
def calc():
    def mex(i):
        D = {}
        for j in X[i]:
            D[G[j]] = 1
        for g in range(N + 1):
            if g not in D:
                return g
    M = int(input())
    X = [[] for _ in range(N)]
    for _ in range(M):
        a, b = map(int, input().split())
        X[N - min(a, b)].append(N - max(a, b))
    G = [0] * N
    for i in range(N):
        G[i] = mex(i)
    H = [0] * 1024
    a = 1
    for i in range(N)[::-1]:
        a = a * A % P
        H[G[i]] = (H[G[i]] + a) % P
    return H

P = 998244353
A = pow(10, 18, P)
N = int(input())
H1, H2, H3 = calc(), calc(), calc()
ans = 0
for i in range(1024):
    if H1[i] == 0: continue
    for j in range(1024):
        if H2[j] == 0: continue
        ans = (ans + H1[i] * H2[j] * H3[i^j]) % P

print(ans)