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:
mod=998244353
inv=pow(2,mod-2,mod)

def xorconv(n,X,Y):
    if n==0:
        res=[(X[0]*Y[0])%mod]
        return res
    x=[X[i]+X[i+2**(n-1)] for i in range(2**(n-1))]
    y=[Y[i]+Y[i+2**(n-1)] for i in range(2**(n-1))]
    z=[X[i]-X[i+2**(n-1)] for i in range(2**(n-1))]
    w=[Y[i]-Y[i+2**(n-1)] for i in range(2**(n-1))]
    res1=xorconv(n-1,x,y)
    res2=xorconv(n-1,z,w)
    former=[(res1[i]+res2[i])*inv for i in range(2**(n-1))]
    latter=[(res1[i]-res2[i])*inv for i in range(2**(n-1))]
    former=list(map(lambda x:x%mod,former))
    latter=list(map(lambda x:x%mod,latter))
    return former+latter

import sys

input=sys.stdin.buffer.readline

N=int(input())

def data():
    edge=[[] for i in range(N)]
    for i in range(int(input())):
        a,b=map(int,input().split())
        if a>b:
            a,b=b,a
        edge[a-1].append(b-1)
    mex=[0 for i in range(N)]
    for i in range(N-1,-1,-1):
        used=[False]*(len(edge[i])+1)
        for pv in edge[i]:
            if mex[pv]<=len(edge[i]):
                used[mex[pv]]=True
        for j in range(len(used)):
            if not used[j]:
                mex[i]=j
                break
    res=[0]*(max(mex)+1)
    for i in range(N):
        res[mex[i]]+=pow(10,18*(i+1),mod)
        res[mex[i]]%=mod

    return res

Xdata=data()
Ydata=data()
Zdata=data()

n=0
m=max(len(Xdata),len(Ydata),len(Zdata))
while 2**n<m:
    n+=1

X=[0 for i in range(2**n)]
Y=[0 for i in range(2**n)]
Z=[0 for i in range(2**n)]

for i in range(len(Xdata)):
    X[i]=Xdata[i]

for i in range(len(Ydata)):
    Y[i]=Ydata[i]

for i in range(len(Zdata)):
    Z[i]=Zdata[i]

YZ=xorconv(n,Y,Z)

ans=0
for i in range(2**n):
    ans+=X[i]*YZ[i]
    ans%=mod

print(ans)