#include<bits/stdc++.h>
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
#define pii pair<ll,ll>
#define rep(i,a,b) for(ll i=(a);i<=(b);++i)
#define per(i,a,b) for(ll i=(a);i>=(b);--i)
using namespace std;
ll read(){
	ll x=0,f=1;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
	return x*f;
}
void write(ll x){
	if(x<0)putchar('-'),x=-x;
	if(x>9)write(x/10);
	putchar(x%10+'0');
}
const ll N=5e5+9,INF=1e16;
ll n,a[N],b[N],x[N],tot,va[N],vb[N],pre[N*2],q[N],l=1,r,vv[N*2];
struct Node{
	ll x,v;
}t[N*2],c[N],d[N];
ld slope(ll i,ll j){
	ll xa=c[i].x,ya=c[i].v,xb=c[j].x,yb=c[j].v;
	if(xa==xb)return -INF;
	return (ya-yb)*1.0/(xb-xa);
}
ll getp(ll x){
	ll l=1,r=tot,p=0;
	while(l<=r){
		ll mid=(l+r)>>1;
		if(vv[mid]<=x)p=mid,l=mid+1;
		else r=mid-1;
	}
	return p;
}
int main(){
//	freopen("gamble.in","r",stdin);
//	freopen("gamble.out","w",stdout);
	n=read();
	rep(i,1,n)a[i]=read(),b[i]=read(),x[i]=read();
	rep(i,1,n)t[++tot]=(Node){a[i],x[i]},t[++tot]=(Node){b[i],x[i]};
	sort(t+1,t+tot+1,[&](Node a,Node b){
		return a.x<b.x||(a.x==b.x&&a.v<b.v);
	});
	ll ru=0;
	rep(i,1,n)ru+=4*x[i];
	rep(i,1,tot)pre[i]=pre[i-1]+t[i].v,vv[i]=t[i].x;
	rep(i,1,n){
		ll p=getp(a[i]);
		va[i]=pre[p]*2;
		p=getp(b[i]);
		vb[i]=pre[p]*2;
	} 
	//max(va[i]+vb[j]-4a[i]b[j])
	a[0]=1;
	ll ans=-INF;
	c[0]=(Node){-4,0}; 
	rep(i,1,n)c[i]=(Node){-4*b[i],vb[i]};
	rep(i,0,n)d[i]=(Node){a[i],va[i]}; 
	sort(c+0,c+n+1,[&](Node a,Node b){
		return a.x<b.x;
	});
	sort(d+0,d+n+1,[&](Node a,Node b){
		return a.x<b.x;
	});
	rep(i,0,n){
		while(l+1<=r&&slope(q[r-1],q[r])>=slope(q[r],i))r--;
		q[++r]=i;
	}
//	if(n<=2000){
//		rep(i,0,n){
//			rep(j,0,n)ans=max(ans,va[i]+c[j].v+c[j].x*a[i]);
//		}
//		write(ans-ru);
//		return 0;
//	} 
	rep(i,0,n){
		while(l+1<=r&&slope(q[l],q[l+1])<=d[i].x)l++;
		ans=max(ans,d[i].v+c[q[l]].v+c[q[l]].x*d[i].x);
	}
	cout<<fixed<<setprecision(12)<<(ans-ru)*0.25;
//	write(ans-ru);
	return 0;
}