#include <bits/stdc++.h>
using namespace std;

const int N=1e5+5;
const int Mod=1e9+7;

int d[N][2];
vector <int> g[N],have[N],cnt1[N],cnt2[N],cnt3[N];
long long inv[N],mul1=1,mul2=1,mul3=1,all=1;
int sum1[N],sum2[N],sum3[N],zero1,zero2,zero3;

void bfs()
{
	queue <pair<int,int> > q;
	q.push(make_pair(1,0)), d[1][0]=0;
	while(!q.empty())
	{
		int x=q.front().first, y=q.front().second;
		q.pop();
		for(auto to:g[x])
			if(d[to][y^1]>1e9)
			{
				d[to][y^1]=d[x][y]+1;
				q.push(make_pair(to,y^1));
			}
	}
}

void Add(int x)
{
	for(auto i:have[x])
	{
		if(!sum1[i] && cnt1[i][x]) zero1--;
		if(sum1[i]) (mul1 *= inv[sum1[i]]) %= Mod;
		sum1[i] += cnt1[i][x];
		if(sum1[i]) (mul1 *= sum1[i]) %= Mod;

		if(!sum2[i] && cnt2[i][x]) zero2--;
		if(sum2[i]) (mul2 *= inv[sum2[i]]) %= Mod;
		sum2[i] += cnt2[i][x];
		if(sum2[i]) (mul2 *= sum2[i]) %= Mod;

		if(!sum3[i] && cnt3[i][x]) zero3--;
		if(sum3[i]) (mul3 *= inv[sum3[i]]) %= Mod;
		sum3[i] += cnt3[i][x];
		if(sum3[i]) (mul3 *= sum3[i]) %= Mod;
	}
}

long long calc()
{
	return all-(zero1?0:mul1)-(zero2?0:mul2)+(zero3?0:mul3);
}

int main()
{
	int k;
	cin >> k;

	int maxn=0;
	for(int i=1;i<=k;i++)
	{
		int n,m;
		scanf("%d %d",&n,&m);
		(all *= n) %= Mod;
		for(int i=1;i<=n;i++)
			g[i].clear(), d[i][0]=d[i][1]=0x3f3f3f3f;

		for(int i=1;i<=m;i++)
		{
			int x,y;
			scanf("%d %d",&x,&y);
			g[x].push_back(y);
			g[y].push_back(x);
		}

		bfs();
		maxn=max(maxn,n);

		for(int j=0;j<n*2;j++)
			cnt1[i].push_back(0), cnt2[i].push_back(0), cnt3[i].push_back(0);

		for(int j=1;j<=n;j++)
		{
			if(d[j][0]<n*2)
				cnt1[i][d[j][0]]++;

			if(d[j][1]<n*2)
				cnt2[i][d[j][1]]++;

			if(max(d[j][0],d[j][1])<n*2)
				cnt3[i][max(d[j][0],d[j][1])]++;
		}

		for(int j=0;j<n*2;j++)
			have[j].push_back(i);
	}

	zero1=zero2=zero3=k;
	inv[1]=1;
	for(int i=2;i<=maxn;i++)
		inv[i]=((-Mod/i)*inv[Mod%i]%Mod+Mod)%Mod;

	long long ans=0;
	for(int i=1;i<maxn*2;i++)
	{
		Add(i-1);
		(ans += calc()) %= Mod;
	}

	Add(maxn*2-1);
	(ans -= calc()*(maxn*2-1)) %= Mod;
	printf("%lld\n",(ans+Mod)%Mod);
	return 0;
}