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 N=1e6+7,p=998244353; bool fl[N];
int n,m,l,f1[N],f2[N],f3[N],g1[N],g2[N],g3[N]; long long g[N]; vector<int>v1[N],v2[N],v3[N];
inline int read(){
	int num=0; char g=getchar(); while(g<48||57<g) g=getchar();
	while(47<g&&g<58) num=(num*10)+g-48,g=getchar(); return num;
}
inline void fwt(int *s){
	for(int d=1;d<l;d=d<<1)
		for(int i=0,r=d<<1;i<l;i+=r)
			for(int j=0;j<d;j++){
				int a=s[i+j],b=s[i+j+d];
				s[i+j]=(a+b)%p,s[i+j+d]=(a-b+p)%p;
			}
}
inline void twf(int *s){
	for(int d=1;d<l;d=d<<1)
		for(int i=0,r=d<<1;i<l;i+=r)
			for(int j=0;j<d;j++){
				int a=s[i+j],b=s[i+j+d];
				s[i+j]=1ll*(a+b)%p*((p+1)/2)%p,s[i+j+d]=1ll*(a-b+p)%p*((p+1)/2)%p;
			}
}
int main(){
	g[0]=1,g[1]=716070898,cin>>n; int u,t;
	for(int i=2;i<=n;i++) g[i]=g[i-1]*g[1]%p;
	m=read();
	for(int i=1;i<=m;i++){
		u=read(),t=read(); if(u>t) swap(u,t); v1[u].push_back(t);
	}
	m=read();
	for(int i=1;i<=m;i++){
		u=read(),t=read(); if(u>t) swap(u,t); v2[u].push_back(t);
	}
	m=read();
	for(int i=1;i<=m;i++){
		u=read(),t=read(); if(u>t) swap(u,t); v3[u].push_back(t);
	}
	for(int i=n-1;i>=1;i--){
		for(int x=0;x<v1[i].size();x++){
			int u=v1[i][x]; fl[f1[u]]=1;
		}
		while(fl[f1[i]]) f1[i]++;
		for(int x=0;x<v1[i].size();x++){
			int u=v1[i][x]; fl[f1[u]]=0;
		}
	}
	for(int i=n-1;i>=1;i--){
		for(int x=0;x<v2[i].size();x++){
			int u=v2[i][x]; fl[f2[u]]=1;
		}
		while(fl[f2[i]]) f2[i]++;
		for(int x=0;x<v2[i].size();x++){
			int u=v2[i][x]; fl[f2[u]]=0;
		}
	}
	for(int i=n-1;i>=1;i--){
		for(int x=0;x<v3[i].size();x++){
			int u=v3[i][x]; fl[f3[u]]=1;
		}
		while(fl[f3[i]]) f3[i]++;
		for(int x=0;x<v3[i].size();x++){
			int u=v3[i][x]; fl[f3[u]]=0;
		}
	}
	l=1; while(l<=n) l=l*2;
	
	for(int i=1;i<=n;i++) g1[f1[i]]=(g1[f1[i]]+g[i])%p,g2[f2[i]]=(g2[f2[i]]+g[i])%p,g3[f3[i]]=(g3[f3[i]]+g[i])%p;
	fwt(g1),fwt(g2),fwt(g3);
	for(int i=0;i<l;i++) g1[i]=1ll*g1[i]*g2[i]%p*g3[i]%p; twf(g1);
	cout<<g1[0]<<endl;
	return 0;
}