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<map>
#include<set>
#include<queue>
#include<cmath>
#include<cstdio>
#include<cctype>
#include<vector>
#include<string>
#include<cstring>
#include<iostream>
#include<algorithm>
#define lc (x<<1)
#define rc (x<<1|1)
#define gc getchar()//(p1==p2&&(p2=(p1=buf)+fread(buf,1,size,stdin),p1==p2)?EOF:*p1++)
#define mk make_pair
#define pi pair<int,int>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
const int N=1e5+10,size=1<<20,mod=998244353;

//char buf[size],*p1=buf,*p2=buf;
template<class o> void qr(o &x) {
	char c=gc; x=0; int f=1;
	while(!isdigit(c)){if(c=='-')f=-1; c=gc;}
	while(isdigit(c)) x=x*10+c-'0',c=gc;
	x*=f;
}
template<class o> void qw(o x) {
	if(x/10) qw(x/10);
	putchar(x%10+'0');
}
template<class o> void pr1(o x) {
	if(x<0)x=-x,putchar('-');
	qw(x); putchar(' ');
}
template<class o> void pr2(o x) {
	if(x<0)x=-x,putchar('-');
	qw(x); puts("");
}

struct edge{int y,next;}a[N];int len,last[N];
void ins(int x,int y) {a[++len]=(edge){y,last[x]};last[x]=len;}

void upd(int &x) {x+=x>>31&mod;}

ll power(ll a,ll b=mod-2) {
	ll c=1;
	for(   ;b;b>>=1,a=a*a%mod)
		if(b&1) c=c*a%mod;
	return c;
}

int n,m,f[N],sum[3][N],sz[3],g[N],num,ans,fir,inv=power(fir=power(10,18));

int main() {
	qr(n);
	for(int graph=0;graph<3;graph++) {
		if(len) memset(last+1,0,n<<2),len=0;
		qr(m); for(int j=1,x,y;j<=m;j++) {
			qr(x),qr(y);
			if(x>y) swap(x,y);
			ins(x,y);
		}
		int now=power(fir,n);
		for(int i=n; i;i--) {
			//求sg函数(f)
			++num;
			for(int k=last[i];k;k=a[k].next)
				g[f[a[k].y]]=num;
			f[i]=0;
			while(g[f[i]]==num) f[i]++;
			sz[graph]=max(sz[graph],f[i]);
			upd(sum[graph][f[i]]+=now-mod);
			now=(ll)now*inv%mod;
		}
	}
	for(int i=0;i<=sz[0];i++)
		for(int j=0,k;j<=sz[1];j++) {
			k=i^j;
			upd(ans+=(ll)sum[0][i]*sum[1][j]%mod*sum[2][k]%mod-mod);
		}
	pr2(ans);
	return 0;
}