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 <cstdio>
#include <algorithm>
#include <vector>

typedef long long LL;
const int Mod = 998244353;
const int MN = 100005, MS = 1 << 9;

inline void Add(int &x, int y) { x -= (x += y) >= Mod ? Mod : 0; }

int N, f1[MN], f2[MN], f3[MN];
std::vector<int> G1[MN], G2[MN], G3[MN];

inline void ReadGraph(std::vector<int> *G) {
	int M;
	scanf("%d", &M);
	while (M--) {
		int x, y;
		scanf("%d%d", &x, &y);
		if (x > y) std::swap(x, y);
		G[x].push_back(y);
	}
}
inline void SolveSG(std::vector<int> *G, int *f) {
	static int buk[MN];
	for (int i = N; i >= 1; --i) {
		for (int x : G[i]) buk[f[x]] = 1;
		f[i] = 0;
		while (buk[f[i]]) ++f[i];
		for (int x : G[i]) buk[f[x]] = 0;
	}
}

int pw[MN];
int b1[MS], b2[MS], b3[MS], Ans;

int main() {
	scanf("%d", &N);
	ReadGraph(G1);
	ReadGraph(G2);
	ReadGraph(G3);
	SolveSG(G1, f1);
	SolveSG(G2, f2);
	SolveSG(G3, f3);
	pw[0] = 1;
	for (int i = 1; i <= N; ++i) pw[i] = pw[i - 1] * 716070898ll % Mod;
	for (int i = 1; i <= N; ++i) Add(b1[f1[i]], pw[i]);
	for (int i = 1; i <= N; ++i) Add(b2[f2[i]], pw[i]);
	for (int i = 1; i <= N; ++i) Add(b3[f3[i]], pw[i]);
	for (int i = 0; i < MS; ++i)
		for (int j = 0; j < MS; ++j)
			Ans = (Ans + (LL)b1[i] * b2[j] % Mod * b3[i ^ j]) % Mod;
	printf("%d\n", Ans);
	return 0;
} // vjudge pink_rabbit