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>
#pragma GCC optimize ("O2")
#pragma GCC optimize ("unroll-loops")
//#pragma GCC optimize("no-stack-protector,fast-math")

using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<pii, int> piii;
typedef pair<ll, ll> pll;
#define debug(x) cerr<<#x<<'='<<(x)<<endl;
#define debugp(x) cerr<<#x<<"= {"<<(x.first)<<", "<<(x.second)<<"}"<<endl;
#define debug2(x, y) cerr<<"{"<<#x<<", "<<#y<<"} = {"<<(x)<<", "<<(y)<<"}"<<endl;
#define debugv(v) {cerr<<#v<<" : ";for (auto x:v) cerr<<x<<' ';cerr<<endl;}
#define all(x) x.begin(), x.end()
#define pb push_back
#define kill(x) return cout<<x<<'\n', 0;

const ld eps=1e-7;
const int inf=1000000010;
const ll INF=10000000000000010LL;
const int mod = 998244353;
const int MAXN = 100010, LOG=20;

ll n, m, k, u, v, x, y, t, a, b, ans;
ll sum[3][MAXN], tav[MAXN];
int mark[MAXN];
int g[MAXN];
vector<int> G[MAXN];

void Solve(int id){
	memset(mark, 0, sizeof(mark));
	memset(g, 0, sizeof(g));
	memset(G, 0, sizeof(G));
	cin>>m;
	while (m--){
		cin>>u>>v;
		if (u>v) swap(u, v);
		G[u].pb(v);
	}
	
	for (int i=n-1; i; i--){
		for (int v:G[i]) mark[g[v]]=i;
		while (mark[g[i]]==i) g[i]++;
	}
	for (int i=1; i<=n; i++) sum[id][g[i]]=(sum[id][g[i]] + tav[i])%mod;
	
}

int main(){
	ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
	//freopen("input.txt", "r", stdin);
	//freopen("output.txt", "w", stdout);
	tav[0]=1;
	tav[1]=1000000000000000000ll%mod;
	for (int i=2; i<MAXN; i++) tav[i]=tav[i-1]*tav[1]%mod;
	cin>>n;
	Solve(0);
	Solve(1);
	Solve(2);
	for (int i=0; sum[0][i]; i++)
		for (int j=0; sum[1][j]; j++)
			ans=(ans + sum[0][i]*sum[1][j]%mod*sum[2][i^j])%mod;
	
	cout<<ans<<'\n';
	
	return 0;
}