/****************************************************************
*	Author: huhao
*	Email: 826538400@qq.com
*	Create time: 2020-02-01 16:07:01
****************************************************************/
#include<stdio.h>
#include<string.h>
#include<math.h>
#include<algorithm>
#define fr(i,a,b) for(int i=(a),end_##i=(b);i<=end_##i;i++)
#define fd(i,a,b) for(int i=(a),end_##i=(b);i>=end_##i;i--)
int read()
{
	int r=0,t=1,c=getchar();
	while(c<'0'||c>'9')
	{
		t=c=='-'?-1:1;
		c=getchar();
	}
	while(c>='0'&&c<='9')
	{
		r=(r<<3)+(r<<1)+(c^48);
		c=getchar();
	}
	return r*t;
}
#define i64 long long
const i64 inf=1ll<<50;
namespace run
{
	const int N=160010;
	i64 n,e,S,T,begin[N],next[N],to[N],w[N],c[N],_n,p1,p2,p3,p4,ans;
	i64 q[10000000],l,r,d[N],pre[N],is[N];
	void add(int u,int v,i64 W,i64 C){ e++; next[e]=begin[u]; begin[u]=e; to[e]=v; w[e]=W; c[e]=C; }
	void Add(int u,int v,i64 W,i64 C){ /*printf("%d %d %d,%d\n",u,v,int(W),int(C));*/ add(u,v,W,C); add(v,u,0,-C); }
#define fo(i,a) for(int i=begin[a];i;i=next[i])
	int bfs()
	{
		fr(i,1,_n) d[i]=inf;
		d[S]=0; q[l=r=0]=S;
		while(l<=r)
		{
			int u=q[l++];
//			printf("%d\n",u);
			is[u]=0;
			fo(i,u) if(w[i]&&d[u]+c[i]<d[to[i]])
			{
				d[to[i]]=d[u]+c[i]; pre[to[i]]=i;
				if(!is[to[i]]){ is[to[i]]=1; q[++r]=to[i]; }
			}
		}
		return d[T]!=inf;
	}
	int main()
	{
		S=++_n; T=++_n; p1=++_n; p2=++_n; p3=++_n; p4=++_n; n=read(); e=1;
		fr(i,1,n)
		{
			int x=read(),y=read(),c=read(); _n++;
			Add(S,_n,c,0); Add(_n,p1,c,x+y); Add(_n,p2,c,x-y); Add(_n,p3,c,-x+y); Add(_n,p4,c,-x-y);
		}
		fr(i,1,n)
		{
			int x=read(),y=read(),c=read(); _n++;
			Add(_n,T,c,0); Add(p1,_n,c,-x-y); Add(p2,_n,c,-x+y); Add(p3,_n,c,x-y); Add(p4,_n,c,x+y);
		}
		while(bfs())
		{
//			fr(i,2,_n) printf("%d%c",int(to[pre[i]^1]),i==_n?'\n':' ');
			i64 mw=inf,t=T;
			while(t!=S){ mw=std::min(mw,w[pre[t]]); t=to[pre[t]^1]; }
			t=T;
			while(t!=S){ ans+=c[pre[t]]*mw; w[pre[t]]-=mw; w[pre[t]^1]+=mw; t=to[pre[t]^1]; }
		}
		printf("%lld\n",-ans);
		return 0;
	}
}
int main()
{
	return run::main();
}
### Prompt

Construct a cpp code solution to the problem outlined:

Snuke is playing with red and blue balls, placing them on a two-dimensional plane.

First, he performed N operations to place red balls. In the i-th of these operations, he placed RC_i red balls at coordinates (RX_i,RY_i). Then, he performed another N operations to place blue balls. In the i-th of these operations, he placed BC_i blue balls at coordinates (BX_i,BY_i). The total number of red balls placed and the total number of blue balls placed are equal, that is, \sum_{i=1}^{N} RC_i = \sum_{i=1}^{N} BC_i. Let this value be S.

Snuke will now form S pairs of red and blue balls so that every ball belongs to exactly one pair. Let us define the score of a pair of a red ball at coordinates (rx, ry) and a blue ball at coordinates (bx, by) as |rx-bx| + |ry-by|.

Snuke wants to maximize the sum of the scores of the pairs. Help him by finding the maximum possible sum of the scores of the pairs.

Constraints

* 1 \leq N \leq 1000
* 0 \leq RX_i,RY_i,BX_i,BY_i \leq 10^9
* 1 \leq RC_i,BC_i \leq 10
* \sum_{i=1}^{N} RC_i = \sum_{i=1}^{N} BC_i
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
RX_1 RY_1 RC_1
RX_2 RY_2 RC_2
\vdots
RX_N RY_N RC_N
BX_1 BY_1 BC_1
BX_2 BY_2 BC_2
\vdots
BX_N BY_N BC_N


Output

Print the maximum possible sum of the scores of the pairs.

Examples

Input

2
0 0 1
3 2 1
2 2 1
5 0 1


Output

8


Input

3
0 0 1
2 2 1
0 0 2
1 1 1
1 1 1
3 3 2


Output

16


Input

10
582463373 690528069 8
621230322 318051944 4
356524296 974059503 6
372751381 111542460 9
392867214 581476334 6
606955458 513028121 5
882201596 791660614 9
250465517 91918758 3
618624774 406956634 6
426294747 736401096 5
974896051 888765942 5
726682138 336960821 3
715144179 82444709 6
599055841 501257806 6
390484433 962747856 4
912334580 219343832 8
570458984 648862300 6
638017635 572157978 10
435958984 585073520 7
445612658 234265014 6


Output

45152033546

### Response

```cpp
/****************************************************************
*	Author: huhao
*	Email: 826538400@qq.com
*	Create time: 2020-02-01 16:07:01
****************************************************************/
#include<stdio.h>
#include<string.h>
#include<math.h>
#include<algorithm>
#define fr(i,a,b) for(int i=(a),end_##i=(b);i<=end_##i;i++)
#define fd(i,a,b) for(int i=(a),end_##i=(b);i>=end_##i;i--)
int read()
{
	int r=0,t=1,c=getchar();
	while(c<'0'||c>'9')
	{
		t=c=='-'?-1:1;
		c=getchar();
	}
	while(c>='0'&&c<='9')
	{
		r=(r<<3)+(r<<1)+(c^48);
		c=getchar();
	}
	return r*t;
}
#define i64 long long
const i64 inf=1ll<<50;
namespace run
{
	const int N=160010;
	i64 n,e,S,T,begin[N],next[N],to[N],w[N],c[N],_n,p1,p2,p3,p4,ans;
	i64 q[10000000],l,r,d[N],pre[N],is[N];
	void add(int u,int v,i64 W,i64 C){ e++; next[e]=begin[u]; begin[u]=e; to[e]=v; w[e]=W; c[e]=C; }
	void Add(int u,int v,i64 W,i64 C){ /*printf("%d %d %d,%d\n",u,v,int(W),int(C));*/ add(u,v,W,C); add(v,u,0,-C); }
#define fo(i,a) for(int i=begin[a];i;i=next[i])
	int bfs()
	{
		fr(i,1,_n) d[i]=inf;
		d[S]=0; q[l=r=0]=S;
		while(l<=r)
		{
			int u=q[l++];
//			printf("%d\n",u);
			is[u]=0;
			fo(i,u) if(w[i]&&d[u]+c[i]<d[to[i]])
			{
				d[to[i]]=d[u]+c[i]; pre[to[i]]=i;
				if(!is[to[i]]){ is[to[i]]=1; q[++r]=to[i]; }
			}
		}
		return d[T]!=inf;
	}
	int main()
	{
		S=++_n; T=++_n; p1=++_n; p2=++_n; p3=++_n; p4=++_n; n=read(); e=1;
		fr(i,1,n)
		{
			int x=read(),y=read(),c=read(); _n++;
			Add(S,_n,c,0); Add(_n,p1,c,x+y); Add(_n,p2,c,x-y); Add(_n,p3,c,-x+y); Add(_n,p4,c,-x-y);
		}
		fr(i,1,n)
		{
			int x=read(),y=read(),c=read(); _n++;
			Add(_n,T,c,0); Add(p1,_n,c,-x-y); Add(p2,_n,c,-x+y); Add(p3,_n,c,x-y); Add(p4,_n,c,x+y);
		}
		while(bfs())
		{
//			fr(i,2,_n) printf("%d%c",int(to[pre[i]^1]),i==_n?'\n':' ');
			i64 mw=inf,t=T;
			while(t!=S){ mw=std::min(mw,w[pre[t]]); t=to[pre[t]^1]; }
			t=T;
			while(t!=S){ ans+=c[pre[t]]*mw; w[pre[t]]-=mw; w[pre[t]^1]+=mw; t=to[pre[t]^1]; }
		}
		printf("%lld\n",-ans);
		return 0;
	}
}
int main()
{
	return run::main();
}
```