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 <vector>
#include <string>
using namespace std;

using cat = long long;

int main() {
	cin.sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	int N;
	cin >> N;
	cat mod = 998244353;
	vector<cat> pw(N+1, 1);
	for(int i = 0; i < 18; i++) pw[1] = pw[1] * 10 % mod;
	for(int i = 2; i <= N; i++) pw[i] = pw[i-1] * pw[1] % mod;
	vector<int> level[3];
	vector<cat> level_w[3];
	int V[3] = {0, 0, 0};
	for(int k = 0; k < 3; k++) {
		int M;
		vector< vector<int> > G(N);
		cin >> M;
		for(int i = 0; i < M; i++) {
			int u, v;
			cin >> u >> v;
			G[--u].push_back(--v);
			G[v].push_back(u);
		}
		level[k].resize(N, 0);
		for(int i = N-1; i >= 0; i--) {
			static vector<int> l_gt(N+1, 0);
			for(auto x : G[i]) if(x > i) l_gt[level[k][x]]++;
			while(l_gt[level[k][i]]) level[k][i]++;
			for(auto x : G[i]) if(x > i) l_gt[level[k][x]]--;
			V[k] = max(V[k], level[k][i]);
		}
		level_w[k].resize(V[k]+1, 0);
		for(int i = N-1; i >= 0; i--) {
			level_w[k][level[k][i]] += pw[i+1];
			if(level_w[k][level[k][i]] >= mod) level_w[k][level[k][i]] -= mod;
		}
	}
	vector< vector< vector<char> > > state(V[0]+1, vector< vector<char> >(V[1]+1, vector<char>(V[2]+1, 0)));
	vector< vector<char> > used[3];
	used[0].resize(V[1]+1, vector<char>(V[2]+1, 0));
	used[1].resize(V[0]+1, vector<char>(V[2]+1, 0));
	used[2].resize(V[0]+1, vector<char>(V[1]+1, 0));
	for(int i = 0; i <= V[0]; i++)
		for(int j = 0; j <= V[1]; j++)
			for(int k = 0; k <= V[2]; k++)
				if(!used[0][j][k] && !used[1][i][k] && !used[2][i][j])
					state[i][j][k] = used[0][j][k] = used[1][i][k] = used[2][i][j] = 1;
	cat ans = 0;
	for(int i = 0; i <= V[0]; i++)
		for(int j = 0; j <= V[1]; j++)
			for(int k = 0; k <= V[2]; k++)
				if(state[i][j][k])
					ans = (ans + level_w[0][i] * level_w[1][j] % mod * level_w[2][k]) % mod;
	cout << ans << "\n";
}