#include<bits/stdc++.h>
using namespace std;
#define double float
int n,m,f[200010],sum[200010],S[200010],T[200010];
vector<int> v[200010];
double d[200010],Z[200010],P[200010];
void solve(int x){
	if(sum[x]>30) return;
	Z[x]+=0.75*P[x]*(d[T[x]]+sum[x]);
	P[x]*=0.25;
	d[x]=min(d[x],Z[x]+(d[S[x]]+sum[x]+2)*P[x]);
}
int main(){
	ios::sync_with_stdio(0);
	cin.tie(0); cout.tie(0);
	priority_queue<pair<double,int> > q;
	int x,y;
	cin>>n>>m;
	for(int i=1;i<=n;i++){
		d[i]=1e9;
		P[i]=1;
	}
	for(int i=1;i<=m;i++){
		cin>>x>>y;
		v[x].push_back(y);
		v[y].push_back(x);
	}
	d[n]=0;
	q.push(make_pair(0,n));
	while(!q.empty()){
		int x=q.top().second; q.pop();
		if(f[x]) continue;
		f[x]=1;
		for(int i=0;i<v[x].size();i++){
			int y=v[x][i];
			if(f[y]) continue;
			sum[y]++;
			if(sum[y]==1) S[y]=x;
			T[y]=x;
			solve(y);
			q.push(make_pair(-d[y],y));
		}
	}
	printf("%.9lf",d[1]);
	return 0;
}