#include<bits/stdc++.h>
#define to edge[i].v
#define mp make_pair
#define rint register int
#define fgx cerr<<"-------------"<<endl
#define N 2333
#define T 2*n+5
#define add(a,b,c,d) adde(a,b,c,d),adde(b,a,0,-(d))
using namespace std;
typedef long long ll;
typedef long double db;
typedef pair<int,int> pii;
void dbg(){cerr<<endl;}
template<typename A,typename... B>void dbg(A x,B... y){cerr<<x<<" ";dbg(y...);}
#define debug(...) cerr<<#__VA_ARGS__<<"=",dbg(__VA_ARGS__)
int head[N],tot=1,vis[N],n,pre[N]; ll dis[N];
struct Edge{int u,v,w,f,next;ll c;}edge[N*100];
inline void adde(int x,int y,int w,int c){edge[++tot]=Edge{x,y,w,0,head[x],c};head[x]=tot;}
inline int spfa()
{	for(rint i=0;i<=T;i++) dis[i]=-1e18; queue<int> q; q.push(0); dis[0]=0; pre[T]=-1;
	while(!q.empty())
	{	int x=q.front(); vis[x]=0; q.pop();
		for(rint i=head[x];i;i=edge[i].next)
		if(dis[to]<dis[x]+edge[i].c&&edge[i].f<edge[i].w)
		{	dis[to]=dis[x]+edge[i].c; pre[to]=i;
			if(!vis[to])q.push(to),vis[to]=1;
		}
	}
	return pre[T]!=-1;
}
inline ll mcmf(int f=0,ll c=0)
{	while(spfa())
	{	int mn=1e9; for(rint i=pre[T];i;i=pre[edge[i].u]) mn=min(mn,edge[i].w-edge[i].f);
		f+=mn; c+=dis[T]*mn; for(rint i=pre[T];i;i=pre[edge[i].u]) edge[i].f+=mn,edge[i^1].f-=mn;
	}
	return c;
}
int main()
{	int x,y,k; cin>>n;
	for(rint i=1;i<=n;i++)
	{	scanf("%d%d%d",&x,&y,&k),add(0,i,k,0);
		add(i,2*n+1,k,x+y),add(i,2*n+2,k,x-y),add(i,2*n+3,k,y-x),add(i,2*n+4,k,-x-y);
	}
	for(rint i=1;i<=n;i++)
	{	scanf("%d%d%d",&x,&y,&k),add(n+i,T,k,0);
		add(2*n+1,n+i,k,-x-y),add(2*n+2,n+i,k,y-x),add(2*n+3,n+i,k,x-y),add(2*n+4,n+i,k,x+y);
	}
	cout<<mcmf();
	return 0;
}

### Prompt

Develop a solution in CPP to the problem described below:

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
#include<bits/stdc++.h>
#define to edge[i].v
#define mp make_pair
#define rint register int
#define fgx cerr<<"-------------"<<endl
#define N 2333
#define T 2*n+5
#define add(a,b,c,d) adde(a,b,c,d),adde(b,a,0,-(d))
using namespace std;
typedef long long ll;
typedef long double db;
typedef pair<int,int> pii;
void dbg(){cerr<<endl;}
template<typename A,typename... B>void dbg(A x,B... y){cerr<<x<<" ";dbg(y...);}
#define debug(...) cerr<<#__VA_ARGS__<<"=",dbg(__VA_ARGS__)
int head[N],tot=1,vis[N],n,pre[N]; ll dis[N];
struct Edge{int u,v,w,f,next;ll c;}edge[N*100];
inline void adde(int x,int y,int w,int c){edge[++tot]=Edge{x,y,w,0,head[x],c};head[x]=tot;}
inline int spfa()
{	for(rint i=0;i<=T;i++) dis[i]=-1e18; queue<int> q; q.push(0); dis[0]=0; pre[T]=-1;
	while(!q.empty())
	{	int x=q.front(); vis[x]=0; q.pop();
		for(rint i=head[x];i;i=edge[i].next)
		if(dis[to]<dis[x]+edge[i].c&&edge[i].f<edge[i].w)
		{	dis[to]=dis[x]+edge[i].c; pre[to]=i;
			if(!vis[to])q.push(to),vis[to]=1;
		}
	}
	return pre[T]!=-1;
}
inline ll mcmf(int f=0,ll c=0)
{	while(spfa())
	{	int mn=1e9; for(rint i=pre[T];i;i=pre[edge[i].u]) mn=min(mn,edge[i].w-edge[i].f);
		f+=mn; c+=dis[T]*mn; for(rint i=pre[T];i;i=pre[edge[i].u]) edge[i].f+=mn,edge[i^1].f-=mn;
	}
	return c;
}
int main()
{	int x,y,k; cin>>n;
	for(rint i=1;i<=n;i++)
	{	scanf("%d%d%d",&x,&y,&k),add(0,i,k,0);
		add(i,2*n+1,k,x+y),add(i,2*n+2,k,x-y),add(i,2*n+3,k,y-x),add(i,2*n+4,k,-x-y);
	}
	for(rint i=1;i<=n;i++)
	{	scanf("%d%d%d",&x,&y,&k),add(n+i,T,k,0);
		add(2*n+1,n+i,k,-x-y),add(2*n+2,n+i,k,y-x),add(2*n+3,n+i,k,x-y),add(2*n+4,n+i,k,x+y);
	}
	cout<<mcmf();
	return 0;
}

```