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



Sample input:
2
1
1 2
1
1 2
1
1 2


Sample output:
46494701

Submission status: Accepted

Solution code:
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))

Submission status: Accepted

Solution code:
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))

Submission status: Accepted

Solution code:
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))

Submission status: Accepted

Solution code:
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))

Submission status: Accepted

Solution code:
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))

Submission status: Accepted

Solution code:
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))

Submission status: Accepted

Solution code:
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)

Submission status: Accepted

Solution code:
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)

Submission status: Accepted

Solution code:
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)

Submission status: Runtime Error

Solution code:
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))

Submission status: Runtime Error

Solution code:
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))

Submission status: Runtime Error

Solution code:
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))

Submission status: Runtime Error

Solution code:
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))

Submission status: Runtime Error

Solution code:
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))

Submission status: Runtime Error

Solution code:
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))