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<cstdio>
using namespace std;
#define N 524289
#define mod 998244353
const int val=1000000000000000000%mod;
inline int M(int x){return (x>=mod)?(x-mod):x;}
inline int M1(int x){return (x<0)?(x+mod):x;}
inline int ksm(int p,int k){int res=1;while(k){if(k&1)res=1ll*res*p%mod;k>>=1;p=1ll*p*p%mod;}return res;}
int n,m,all,len,s[N],f[N],g[N],h[N],cnt=0;
struct Edge{int to,next;}e[N<<1];
inline void AddEdge(int x,int y){e[++cnt]=(Edge){y,h[x]};h[x]=cnt;}
inline void FWT(int f[],int len)
{
	int i,j,x,y;
	for(int j=1;j<len;j<<=1)
	for(int i=0;i<len;i++)if(i&j){x=f[i^j];y=f[i];f[i^j]=M(x+y);f[i]=M1(x-y);}
}
inline void IFWT(int f[],int len)
{
	int i,j,x,y,inv;
	for(int j=1;j<len;j<<=1)
	for(int i=0;i<len;i++)if(i&j){x=f[i^j];y=f[i];f[i^j]=M(x+y);f[i]=M1(x-y);}
	inv=ksm(len,mod-2);for(i=0;i<len;i++)f[i]=1ll*f[i]*inv%mod;
}
int tmp[N],P[N];
inline void solve()
{
	scanf("%d",&m);int i,x,y;
	for(i=1;i<=m;i++){scanf("%d%d",&x,&y);AddEdge(x,y);AddEdge(y,x);}
	s[n]=0;
	for(x=n-1;x>=1;x--)
	{
		for(i=h[x];i;i=e[i].next)if((y=e[i].to)>=x)tmp[s[y]]=1;
		s[x]=0;while(tmp[s[x]])++s[x];
		for(i=h[x];i;i=e[i].next)if((y=e[i].to)>=x)tmp[s[y]]=0;
	}
	for(i=1;i<=n;i++)f[s[i]]=M(f[s[i]]+P[i]);FWT(f,len);
	for(i=0;i<len;i++)g[i]=1ll*g[i]*f[i]%mod;
	for(i=1;i<=n;i++)s[i]=h[i]=0;cnt=0;
	for(i=0;i<len;i++)f[i]=0;
}
int main(){
	P[0]=1;for(int i=1;i<N;i++)P[i]=1ll*P[i-1]*val%mod;
	scanf("%d",&n);all=3*n;len=1;while(len<all)len<<=1;
	g[0]=1;FWT(g,len);solve();solve();solve();IFWT(g,len);printf("%d",g[0]);return 0;
}