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>
#define rep(i,a,b) for(int i=(a);i<=(b);i++)
#define per(i,a,b) for(int i=(a);i>=(b);i--)
#define REP(i,n) for(int i=0;i<(n);i++)
#define fi first
#define se second
#define pb push_back
#define mp make_pair
using namespace std;
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef long long ll;

template<class T> void read(T &x){
	int f=0; x=0; char ch=getchar();
	for(;!isdigit(ch);ch=getchar()) f|=(ch=='-');
	for(;isdigit(ch);ch=getchar()) x=x*10+ch-'0';
	if(f) x=-x;
}

const int N=100005,mod=998244353,M=1<<10;
const int bas=int(1000000000000000000ll%mod);
int pw[N],f[N],g[M],dp[M],ndp[M],vis[M];
int n,A,B,a,b,m;
vi e[N];

int main(){
	read(n);
	pw[0]=1;
	rep(i,1,n) pw[i]=(ll)pw[i-1]*bas%mod;
	dp[0]=1;
	REP(t,3){
		rep(i,1,n) e[i].clear();
		read(m);
		rep(i,1,m){
			read(a),read(b);
			if(a>b) swap(a,b);
			e[a].pb(b);
		}
		memset(g,0,sizeof g);
		per(i,n,1){
			f[i]=0;
			for(auto j:e[i]) vis[f[j]]=1;
			while(vis[f[i]]) f[i]++;
			g[f[i]]=(g[f[i]]+pw[i])%mod;
			for(auto j:e[i]) vis[f[j]]=0;
		}
		memset(ndp,0,sizeof ndp);
		REP(i,M) REP(j,M)
			ndp[i^j]=(ndp[i^j]+(ll)dp[i]*g[j])%mod;
		memcpy(dp,ndp,sizeof dp);
	}
	cout<<dp[0]<<endl;
	return 0;
}