Problem: 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.

Examples

Input

2
1
1 2
1
1 2
1
1 2


Output

46494701


Input

3
3
1 3
1 2
3 2
2
2 1
2 3
1
2 1


Output

883188316


Input

100000
1
1 2
1
99999 100000
1
1 100000


Output

318525248

Solution (in PYTHON3):

Solution:
import sys
input = sys.stdin.readline

mod=998244353

N=int(input())
M1=int(input())
E1=[[] for i in range(N+1)]
for i in range(M1):
    x,y=map(int,input().split())
    E1[x].append(y)
    E1[y].append(x)

M2=int(input())
E2=[[] for i in range(N+1)]
for i in range(M2):
    x,y=map(int,input().split())
    E2[x].append(y)
    E2[y].append(x)

M3=int(input())
E3=[[] for i in range(N+1)]
for i in range(M3):
    x,y=map(int,input().split())
    E3[x].append(y)
    E3[y].append(x)

G1=[-1]*(N+1)
G1[N]=0
for i in range(N-1,-1,-1):
    GS=set()
    for to in E1[i]:
        GS.add(G1[to])
    for j in range(N+1):
        if j in GS:
            continue
        else:
            G1[i]=j
            break

G2=[-1]*(N+1)
G2[N]=0
for i in range(N-1,-1,-1):
    GS=set()
    for to in E2[i]:
        GS.add(G2[to])
    for j in range(N+1):
        if j in GS:
            continue
        else:
            G2[i]=j
            break

G3=[-1]*(N+1)
G3[N]=0
for i in range(N-1,-1,-1):
    GS=set()
    for to in E3[i]:
        GS.add(G3[to])
    for j in range(N+1):
        if j in GS:
            continue
        else:
            G3[i]=j
            break

from collections import Counter
C1=Counter()
C2=Counter()
C3=Counter()

for i in range(1,N+1):
    C1[G1[i]]=(C1[G1[i]]+pow(10,18*i,mod))%mod
    C2[G2[i]]=(C2[G2[i]]+pow(10,18*i,mod))%mod
    C3[G3[i]]=(C3[G3[i]]+pow(10,18*i,mod))%mod
        
C12=Counter()

for c1 in C1:
    for c2 in C2:
        C12[c1^c2]=(C12[c1^c2]+C1[c1]*C2[c2])%mod

ANS=0
for c3 in C3:
    ANS=(ANS+C3[c3]*C12[c3])%mod

print(ANS)