#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define M 20005
#define inf 998244353
struct edge{
    int t,v,f,nxt;
}e[M];
int head[M],tot=1;
void add(int st,int t,int v,int f) {
    e[++tot].nxt=head[st],e[tot].t=t,e[tot].v=v,e[tot].f=f,head[st]=tot;
    e[++tot].nxt=head[t],e[tot].t=st,e[tot].v=-v,e[tot].f=0,head[t]=tot;
}
int n,s,t;
ll ans;
int d[M],vis[M],pre[M],F,L;
ll dis[M];
bool spfa() {
    int tp=0;
    for(int i=1;i<=t;i++) vis[i]=0,dis[i]=-1e18;
    F=L=0;
    d[++L]=s,dis[s]=0;
    do{
	int p=d[++F];
	vis[p]=0;
	for(int i=head[p];i;i=e[i].nxt)
	    {
		int to=e[i].t;
		if(!e[i].f) continue ;
		if(dis[to]<dis[p]+e[i].v)
		    {
			if(to==t) tp=1;
			dis[to]=dis[p]+e[i].v,pre[to]=i^1;
			if(!vis[to]) d[++L]=to,vis[to]=1;
		    }
	    }
    }while(F<L);
    if(!tp) return 0;
    int p=t,Mf=inf;
    while(p!=s)
	{
	    Mf=min(Mf,e[pre[p]^1].f);
	    p=e[pre[p]].t;
	}
    p=t;
    while(p!=s)
	{
	    e[pre[p]^1].f-=Mf;
	    e[pre[p]].f+=Mf;
	    ans+=1ll*e[pre[p]^1].v*Mf;
	    p=e[pre[p]].t;
	}
    return 1;
}
void work() {
    while(spfa()) ;
    cout<<ans<<'\n';
}
int main()
{
    cin>>n;
    s=n*2+9,t=s+1;
    for(int i=1,x,y,c;i<=n;i++)
	{
	    cin>>x>>y>>c;
	    add(s,i,0,c);
	    add(i,n*2+1,x+y,inf);
	    add(i,n*2+2,x-y,inf);
	    add(i,n*2+3,-x+y,inf);
	    add(i,n*2+4,-x-y,inf);
	}
    for(int i=1,x,y,c;i<=n;i++)
	{
	    cin>>x>>y>>c;
	    add(i+n,t,0,c);
	    add(n*2+5,i+n,x+y,inf);
	    add(n*2+6,i+n,x-y,inf);
	    add(n*2+7,i+n,-x+y,inf);
	    add(n*2+8,i+n,-x-y,inf);
	}
    add(n*2+1,n*2+8,0,inf);
    add(n*2+2,n*2+7,0,inf);
    add(n*2+3,n*2+6,0,inf);
    add(n*2+4,n*2+5,0,inf);
    work();
    return 0;
}
### Prompt

Your challenge is to write a cpp solution to the following problem:

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>
using namespace std;
#define ll long long
#define M 20005
#define inf 998244353
struct edge{
    int t,v,f,nxt;
}e[M];
int head[M],tot=1;
void add(int st,int t,int v,int f) {
    e[++tot].nxt=head[st],e[tot].t=t,e[tot].v=v,e[tot].f=f,head[st]=tot;
    e[++tot].nxt=head[t],e[tot].t=st,e[tot].v=-v,e[tot].f=0,head[t]=tot;
}
int n,s,t;
ll ans;
int d[M],vis[M],pre[M],F,L;
ll dis[M];
bool spfa() {
    int tp=0;
    for(int i=1;i<=t;i++) vis[i]=0,dis[i]=-1e18;
    F=L=0;
    d[++L]=s,dis[s]=0;
    do{
	int p=d[++F];
	vis[p]=0;
	for(int i=head[p];i;i=e[i].nxt)
	    {
		int to=e[i].t;
		if(!e[i].f) continue ;
		if(dis[to]<dis[p]+e[i].v)
		    {
			if(to==t) tp=1;
			dis[to]=dis[p]+e[i].v,pre[to]=i^1;
			if(!vis[to]) d[++L]=to,vis[to]=1;
		    }
	    }
    }while(F<L);
    if(!tp) return 0;
    int p=t,Mf=inf;
    while(p!=s)
	{
	    Mf=min(Mf,e[pre[p]^1].f);
	    p=e[pre[p]].t;
	}
    p=t;
    while(p!=s)
	{
	    e[pre[p]^1].f-=Mf;
	    e[pre[p]].f+=Mf;
	    ans+=1ll*e[pre[p]^1].v*Mf;
	    p=e[pre[p]].t;
	}
    return 1;
}
void work() {
    while(spfa()) ;
    cout<<ans<<'\n';
}
int main()
{
    cin>>n;
    s=n*2+9,t=s+1;
    for(int i=1,x,y,c;i<=n;i++)
	{
	    cin>>x>>y>>c;
	    add(s,i,0,c);
	    add(i,n*2+1,x+y,inf);
	    add(i,n*2+2,x-y,inf);
	    add(i,n*2+3,-x+y,inf);
	    add(i,n*2+4,-x-y,inf);
	}
    for(int i=1,x,y,c;i<=n;i++)
	{
	    cin>>x>>y>>c;
	    add(i+n,t,0,c);
	    add(n*2+5,i+n,x+y,inf);
	    add(n*2+6,i+n,x-y,inf);
	    add(n*2+7,i+n,-x+y,inf);
	    add(n*2+8,i+n,-x-y,inf);
	}
    add(n*2+1,n*2+8,0,inf);
    add(n*2+2,n*2+7,0,inf);
    add(n*2+3,n*2+6,0,inf);
    add(n*2+4,n*2+5,0,inf);
    work();
    return 0;
}
```