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<bits/stdc++.h>
using namespace std;
const int maxn=100100,mod=998244353;
inline void Add(int &a,int b){a=a+b>=mod?a+b-mod:a+b;}
inline int ksm(int a,int b)
{
	int res=1;
	for(;b;b>>=1,a=1ll*a*a%mod) if(b&1) res=1ll*res*a%mod;
	return res;
}
int N;
struct Graph
{
	vector<int> V[maxn];int M,sg[maxn],sum[512];
	inline void read()
	{
		scanf("%d",&M);
		for(int i=1,A,B;i<=M;i++)
		{
			scanf("%d%d",&A,&B);
			if(A>B) swap(A,B);
			V[A].push_back(B);
		}
	}
	inline void Getsg()
	{
		for(int i=N;i;i--)
		{
			set<int> S;
			for(int j=0;j<(int)V[i].size();j++) S.insert(sg[V[i][j]]);
			while(S.count(sg[i])) sg[i]++;
			Add(sum[sg[i]],ksm(10,i*18));
		}
	}
}G[3];
int main()
{
	scanf("%d",&N);
	G[0].read();G[1].read();G[2].read();
	G[0].Getsg();G[1].Getsg();G[2].Getsg();
	int ans=0;
	for(int A=0;A<512;A++) for(int B=0;B<512;B++)
		Add(ans,1ll*G[0].sum[A]*G[1].sum[B]%mod*G[2].sum[A^B]%mod);
	cout<<ans<<endl;
	return 0;
}