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<cctype>
#include<cstdio>
#include<vector>
const int N=100007,M=512,P=998244353,base=1000000000000000000%P;
int read(){int x=0,c=getchar();while(isspace(c))c=getchar();while(isdigit(c))(x*=10)+=c&15,c=getchar();return x;}
void inc(int&a,int b){a+=b-P,a+=a>>31&P;}
int mul(int a,int b){return 1ll*a*b%P;}
int n;
struct graph
{
    int f[N],g[M],vis[M];std::vector<int>e[N];
    void input()
    {
	for(int m=read(),u,v;m;--m) u=read(),v=read(),e[std::min(u,v)].push_back(std::max(u,v));
	for(int u=n;u;--u)
	{
	    for(int v:e[u]) vis[f[v]]=1;
	    while(vis[f[u]]) ++f[u];
	    for(int v:e[u]) vis[f[v]]=0;
	}
	for(int i=1,x=1;i<=n;++i) x=mul(x,base),inc(g[f[i]],x);
    }
}a[3];
int main()
{
    n=read();int ans=0;
    for(int i=0;i<3;++i) a[i].input();
    for(int i=0;i<512;++i) for(int j=0;j<512;++j) inc(ans,1ll*a[0].g[i]*a[1].g[j]%P*a[2].g[i^j]%P);
    printf("%d",ans);
}