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 ljc 998244353
using namespace std;
#define gc getchar
inline ll read(){
    register ll x=0,f=1;char ch=gc();
    while (!isdigit(ch)){if (ch=='-') f=-1;ch=gc();}
    while (isdigit(ch)){x=(x<<3)+(x<<1)+ch-'0';ch=gc();}
    return (f==1)?x:-x;
}
ll pw[1010101],cac[4][1010101];
int n,m,sg[1010101],vis[1010101];
vector<int> e[1010101];
inline void solve(int id){
	for (int i=1;i<=n;i++) e[i].clear(),sg[i]=vis[i]=0;
	m=read();
	for (int i=1;i<=m;i++){
		int x=read(),y=read();
		e[min(x,y)].push_back(max(x,y));
	}
	for (int i=n;i;i--){
		for (auto v:e[i]) vis[sg[v]]=1;
		while (vis[sg[i]]) sg[i]++;
		for (auto v:e[i]) vis[sg[v]]=0;
		cac[id][sg[i]]=(cac[id][sg[i]]+pw[i])%ljc;
	}
}
signed main(){
	n=read();
	pw[0]=1,pw[1]=1000000000000000000%ljc;
	for (int i=2;i<=n;i++) pw[i]=pw[i-1]*pw[1]%ljc;
	solve(1);
	solve(2);
	solve(3);
	ll _=0;
	for (int i=0;i<=1000;i++)
		for (int j=0;j<=1000;j++) _=(_+cac[1][i]*cac[2][j]%ljc*cac[3][i^j]%ljc)%ljc;
	cout<<_;
	return 0;
}