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 ll long long
#define lld long double
using namespace std;
template<typename tn> void read(tn &a){
	tn x=0,f=1; char c=' ';
	for(;!isdigit(c);c=getchar()) if(c=='-') f=-1;
	for(;isdigit(c);c=getchar()) x=x*10+c-'0';
	a=x*f;
}
const int N = 101000,mod = 998244353;
ll p[N];
int n;
struct graph{
	int hsh[N],f[N],m,n;
	ll h[N];
	vector<int> e[N];
	void init(int S){
		n=S;
		read(m);
		for(int i=1;i<=m;i++){
			int x,y;read(x);read(y);
			if(x>y) swap(x,y);
			e[x].push_back(y);
		}
		for(int i=n;i;i--){
			for(int v:e[i]) hsh[f[v]]++;
			while(hsh[f[i]]) f[i]++;
			h[f[i]]=(h[f[i]]+p[i])%mod;
			for(int v:e[i]) hsh[f[v]]--;
		}
	}
}Gx,Gy,Gz;
int main(){
	read(n);
	p[0]=1;p[1]=1000000000000000000ll%mod;
	for(int i=2;i<=n;i++) p[i]=p[i-1]*p[1]%mod;
	Gx.init(n);
	Gy.init(n);
	Gz.init(n);
	int K=500;
	ll ans=0;
	for(int i=0;i<=K;i++)
		for(int j=0;j<=K;j++)
			ans=(ans+Gx.h[i]*Gy.h[j]%mod*Gz.h[i^j])%mod;
	cout<<ans<<'\n';
	return 0;
}