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>

const int MAX_N = int(1e5) + 10;
const int mod = 998244353;

int n, m, base;

struct Graph {
	int sg[MAX_N], cnt[MAX_N], ext[MAX_N];
	std::vector<int> edges[MAX_N];

	void addEdge(int x, int y) {
		if (x > y) std::swap(x, y);
		edges[x].emplace_back(y);
	}

	void getSG(int x) {
		for (auto p : edges[x]) ext[sg[p]] = 1;
		while (ext[sg[x]]) ++sg[x];
		for (auto p : edges[x]) ext[sg[p]] = 0;
	}

	void init() {
		int x = 1;
		for (int i = 1; i <= n; ++i) {
			x = 1LL * base * x % mod;
			(cnt[sg[i]] += x) %= mod;
		}
	}
} g[3];

int main() {
	base = 1;
	for (int i = 1; i <= 18; ++i) {
		base = 1LL * base * 10 % mod;
	}
	
	scanf("%d", &n);
	for (int i = 0; i < 3; ++i) {
		scanf("%d", &m);
		while (m--) {
			int x, y;
			scanf("%d%d", &x, &y);
			g[i].addEdge(x, y);
		}
		for (int j = n; j; --j) {
			g[i].getSG(j);
		}
		g[i].init();
	}
	
	int ans = 0;
	for (int i = 0; i < 512; ++i) {
		for (int j = 0; j < 512; ++j) {
			int d = 1LL * g[0].cnt[i] * g[1].cnt[j] % mod * g[2].cnt[i ^ j] % mod;
			(ans += d) %= mod;
		}
	}
	printf("%d\n", ans);
}