//Author: Kevin
#include<bits/stdc++.h>
//#pragma GCC optimize("O2")
using namespace std;
#define rep(i, n) for(int i = 0; i < (n); ++i)
#define ll long long
#define ull unsigned ll
#define pb emplace_back
#define mp make_pair
#define ALL(x) (x).begin(),(x).end()
#define rALL(x) (x).rbegin(),(x).rend()
#define srt(x) sort(ALL(x))
#define rev(x) reverse(ALL(x))
#define rsrt(x) sort(rALL(x))
#define sz(x) (int)(x.size())
#define inf 0x3f3f3f3f
#define pii pair<int,int>
#define lb(v,x) (int)(lower_bound(ALL(v),x)-v.begin())
#define ub(v,x) (int)(upper_bound(ALL(v),x)-v.begin())
#define uni(v) v.resize(unique(ALL(v))-v.begin())
#define longer __int128_t
#define ls ((x)<<1)
#define rs (ls|1)
#define ld long double
void die(string S){puts(S.c_str());exit(0);}
const ll thres=1e18;
ll h[300300],u[300300],v[300300];
ll val[300300];
int ind[300300];

int n;
ld A[300300<<2];
ll B[300300<<2],tim[300300<<2],tag[300300<<2];
void pushdown(int x,int l,int r);
void pushup(int x,int l,int r)
{
	int mid=(l+r)/2;
	pushdown(ls,l,mid);
	pushdown(rs,mid+1,r);
	tim[x]=min(tim[ls],tim[rs]);
	tim[x]=min(tim[x],thres);
	ld vls=A[ls]+sqrtl(B[ls]);
	ld vrs=A[rs]+sqrtl(B[rs]);
	if(vls<vrs)
	{
		A[x]=A[ls];
		B[x]=B[ls];
		if(B[rs]>B[ls])
			if(A[ls]+sqrtl(B[ls]+tim[x])>A[rs]+sqrtl(B[rs]+tim[x]))
			{
				ll l=0,r=tim[x];
				while(l<r)
				{
					ll mid=(l+r)/2;
					if(A[ls]+sqrtl(B[ls]+mid)>A[rs]+sqrtl(B[rs]+mid))
						r=mid;
					else
						l=mid+1;
				}
				tim[x]=l;
			}
	}
	else
	{
		A[x]=A[rs];
		B[x]=B[rs];
		if(B[ls]>B[rs])
			if(A[rs]+sqrtl(B[rs]+tim[x])>A[ls]+sqrtl(B[ls]+tim[x]))
			{
				ll l=0,r=tim[x];
				while(l<r)
				{
					ll mid=(l+r)/2;
					if(A[ls]+sqrtl(B[ls]+mid)<A[rs]+sqrtl(B[rs]+mid))
						r=mid;
					else
						l=mid+1;
				}
				tim[x]=l;
			}
	}
}
void pushdown(int x,int l,int r)
{
	if(l==r)
	{
		B[x]+=tag[x];
		tag[x]=0;
		return ;
	}
	if(tag[x]<tim[x])
	{
		tim[x]-=tag[x];
		tag[ls]+=tag[x];
		tag[rs]+=tag[x];
		B[x]+=tag[x];
		tag[x]=0;
		pushup(x,l,r);
		return ;
	}
	int mid=(l+r)/2;
	tag[ls]+=tag[x];
	tag[rs]+=tag[x];
	tag[x]=0;
	pushdown(ls,l,mid);
	pushdown(rs,mid+1,r);
	pushup(x,l,r);
}
void modify(int x,int l,int r,int p,ld vA,ll vB)
{
	pushdown(x,l,r);
	if(l==r)
	{
		A[x]=vA;
		B[x]=vB;
		return ;
	}
	int mid=(l+r)/2;
	if(p<=mid)
		modify(ls,l,mid,p,vA,vB);
	else
		modify(rs,mid+1,r,p,vA,vB);
	pushup(x,l,r);
}
ld query(int x,int l,int r,int ql,int qr)
{
	pushdown(x,l,r);
	if(l==ql&&r==qr)
		return A[x]+sqrtl(B[x]);
	int mid=(l+r)/2;
	if(qr<=mid)
		return query(ls,l,mid,ql,qr);
	if(ql>mid)
		return query(rs,mid+1,r,ql,qr);
	return min(query(ls,l,mid,ql,mid),query(rs,mid+1,r,mid+1,qr));
}

vector<ll> xs;
int cx;
const ld biginf = 1e100;
struct ds{
	ll x; ld y;
	ds(ll _x = 0, ld _y = -biginf){
		x = _x, y = _y;
	}
	ld gety(ll p){
		if(p < x) return -biginf;
		return sqrtl(p - x) + y;
	}
} dat[1200120];
namespace lct{
	void ins(ll tl, ll tr, ds cur, int l, int r, int k){
//		if(k == 1){
//			cout << "ins " << tl << " " << tr << " " << "(" << cur.x << " " << cur.y << ")\n";
//		}
		ll xl = xs[l], xr = xs[r];
		if(tl > xr || xl > tr) return ;
		int mid = (l+r) >> 1;
		if(tl <= xl && xr <= tr){
			if(cur.gety(xs[mid]) >= dat[k].gety(xs[mid])) swap(cur, dat[k]);
			if(l == r) return ;
			if(cur.gety(xs[l]) >= dat[k].gety(xs[l])) ins(tl, tr, cur, l, mid, k+k);
			if(cur.gety(xs[r]) >= dat[k].gety(xs[r])) ins(tl, tr, cur, mid+1, r, k+k+1);
		} else {
			ins(tl, tr, cur, l, mid, k+k);
			ins(tl, tr, cur, mid+1, r, k+k+1);
		}
	}
	ld qry(int p, int l, int r, int k){
		ld ret = dat[k].gety(xs[p]);
		if(l < r){
			int mid = (l+r) >> 1;
			ret = max(ret, (p <= mid) ? qry(p, l, mid, k+k) : qry(p, mid+1, r, k+k+1));
		}
		return ret;
	}
}

ld f[300300];

int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	cin>>n;
	for(int i=1;i<=n;i++)
		cin>>h[i]>>v[i]>>u[i];
	for(int i=1;i<=n;i++)
		val[i]=2*h[i]+v[i]*v[i];

	for(int i = 1; i <= n; ++i)
		xs.push_back(u[i]*u[i] + 2*h[i]);
	sort(xs.begin(), xs.end());
	xs.resize(cx = (int)(unique(xs.begin(), xs.end()) - xs.begin()));

	vector<pair<ll,int>> vec;
	for(int i=1;i<=n;i++)
		vec.pb(val[i],i);
	srt(vec);
	for(int i=1;i<=n;i++)
		ind[vec[i-1].second]=i;
	for(int i=1;i<(300300<<2);i++)
		A[i]=1e100;
	memset(tim,0x3f,sizeof(tim));
	modify(1,1,n,ind[n],-v[n],v[n]*v[n]);

	f[n] = 0;
	lct::ins(2*h[n], 2*h[n] + v[n]*v[n], ds(2*h[n], - f[n]), 0, cx-1, 1);

	for(int i=n-1;i>=1;i--)
	{
		tag[1]+=2*(h[i+1]-h[i]);
		int pos=lb(vec,mp(2*h[i]+u[i]*u[i]+1,0));
//		cerr<<"!   "<<i<<" "<<pos<<" "<<ind[i]<<endl;
		ld val=query(1,1,n,1,pos);
//		cerr << val << endl;

		int np = (int)(lower_bound(xs.begin(), xs.end(), u[i]*u[i] + 2*h[i]) - xs.begin());
//		cout << lct::qry(np, 0, cx-1, 1) << "\n";
//		f[i]=val;
		f[i] = val = min(val, u[i] - lct::qry(np, 0, cx-1, 1));

//		cerr<<f[i]<<endl;
		if(i==1)
		{
			if(f[i] > 1e30)
				cout << "-1\n";
			else
				cout<<fixed<<setprecision(20)<<f[i]<<endl;
			return 0;
		}
		modify(1,1,n,ind[i],f[i]-v[i],v[i]*v[i]);

		lct::ins(2*h[i], 2*h[i] + v[i]*v[i], ds(2*h[i], - f[i]), 0, cx-1, 1);
	}
	return 0;
}