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>
#define int long long
using namespace std;
const int N=1e5+10,mod=998244353,B=1e18;
int n,ans,tmp=B%mod;
struct Graph{
	int m,cnt;
	int head[N],to[N],nxt[N],vis[N],sg[N],sum[N];
	void add(int u,int v){
		to[++cnt]=v,nxt[cnt]=head[u],head[u]=cnt;
	}
	void init(){
		scanf("%lld",&m);
		for(int i=1;i<=m;i++){ int u,v; scanf("%lld%lld",&u,&v),add(min(u,v),max(u,v)); }
		for(int i=n;i>=1;i--){
			for(int j=head[i];j;j=nxt[j]) vis[sg[to[j]]]=1;
			while(vis[sg[i]]) sg[i]++;
			for(int j=head[i];j;j=nxt[j]) vis[sg[to[j]]]=0; 
		}
		for(int i=1,mul=1;i<=n;i++) mul=mul*tmp%mod,sum[sg[i]]=(sum[sg[i]]+mul)%mod;
	}
}G[3];
signed main(){
	scanf("%lld",&n); 
	for(int i=0;i<3;i++) G[i].init();
	for(int i=0;i<512;i++) for(int j=0;j<512;j++) ans=(ans+G[0].sum[i]*G[1].sum[j]%mod*G[2].sum[i^j]%mod)%mod;
	printf("%lld",ans);
}