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:
//%std
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
inline int read()
{
	int out = 0, fh = 1;
	char jp = getchar();
	while ((jp > '9' || jp < '0') && jp != '-')
		jp = getchar();
	if (jp == '-')
		fh = -1, jp = getchar();
	while (jp >= '0' && jp <= '9')
		out = out * 10 + jp - '0', jp = getchar();
	return out * fh;
}
const int P = 998244353;
int add(int a, int b)
{
	return a + b >= P ? a + b - P : a + b;
}
void inc(int &a, int b)
{
	a = add(a, b);
}
int mul(int a, int b)
{
	return 1LL * a * b % P;
}
int fpow(int a, int b)
{
	int res = 1;
	while (b)
	{
		if (b & 1)
			res = mul(res, a);
		a = mul(a, a);
		b >>= 1;
	}
	return res;
}
const int N = 1e5 + 10;
vector<int> G[3][N];
int n, m[3], mx = 0, SG[3][N], sum[3][N], cnt[3][N], bucket[N]; 
int main()
{
	n = read();
	for (int k = 0; k < 3; ++k)
	{
		m[k] = read();
		for (int i = 1; i <= m[k]; ++i)
		{
			int u = read(), v = read();
			if (u > v)
				swap(u, v);
			G[k][u].push_back(v);
		}
		for (int i = n; i >= 1; --i)
		{
			for (int x : G[k][i])
				bucket[SG[k][x]] = 1;
			for (int val = 0; val <= mx + 1; ++val)
				if (!bucket[val])
				{
					SG[k][i] = val;
					mx = max(mx, val);
					break;
				}
			inc(sum[k][SG[k][i]], fpow(10, 18 * i));
			for (int x : G[k][i])
				bucket[SG[k][x]] = 0;
		}
	}
	int ans = 0;
	for (int x = 0; x <= mx; ++x) if (sum[0][x])
		for (int y = 0; y <= mx; ++y) if (sum[1][y])
			inc(ans, mul(sum[0][x], mul(sum[1][y], sum[2][x ^ y])));
	printf("%d\n", ans);
	return 0;
}