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 CPP):

Solution:
#include<iostream>
#include<vector>
#include<algorithm>
#include<set>
using namespace std;
int N;
long mod=998244353;
long v[1<<17];
vector<long>calc()
{
	int M;cin>>M;
	vector<vector<int> >G(N+1);
	for(int i=0;i<M;i++)
	{
		int u,v;cin>>u>>v;
		if(u>v)swap(u,v);
		G[u].push_back(v);
	}
	vector<long>ret(500,0L);
	vector<int>gru(N+1);
	for(int i=N;i;i--)
	{
		set<int>S;
		for(int v:G[i])S.insert(gru[v]);
		int id=0;
		while(S.find(id)!=S.end())id++;
		gru[i]=id;
		(ret[id]+=v[i])%=mod;
	}
	return ret;
}
int main()
{
	cin>>N;
	v[0]=1;
	for(int i=1;i<=N;i++)v[i]=v[i-1]*716070898%mod;
	vector<long>A=calc();
	vector<long>B=calc();
	vector<long>C=calc();
	long ans=0;
	for(int i=0;i<500;i++)for(int j=0;j<500;j++)for(int k=0;k<500;k++)
	{
		if((i^j^k)==0)(ans+=A[i]*B[j]%mod*C[k]%mod)%=mod;
	}
	cout<<ans<<endl;
}