#include<bits/stdc++.h>
using namespace std;
const int N=1e5+10;
typedef long long ll;
const int inf=1e9;
const ll Inf=1e18;

int gi() {
	int x=0,o=1;char ch=getchar();
	while((ch<'0'||ch>'9')&&ch!='-') ch=getchar();
	if(ch=='-') o=-1,ch=getchar();
	while(ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar();
	return x*o;
}

int to[N<<1],ww[N<<1],cost[N<<1],nxt[N<<1],tt=1,h[N],s,t,cur[N];
ll dis[N],ans=0;
bool vis[N];

void adde(int u,int v,int w,int c) {
	to[++tt]=v,ww[tt]=w,cost[tt]=c,nxt[tt]=h[u],h[u]=tt;
	to[++tt]=u,ww[tt]=0,cost[tt]=-c,nxt[tt]=h[v],h[v]=tt;
}

bool spfa() {
	memset(dis,0x3f,sizeof(dis));
	memset(vis,0,sizeof(vis));
	deque<int> q;q.push_back(s);dis[s]=0;
	while(!q.empty()) {
		int u=q.front();q.pop_front();vis[u]=0;
		for(int i=h[u],v;v=to[i],i;i=nxt[i]) {
			if(ww[i]&&dis[v]>dis[u]+cost[i]) {
				dis[v]=dis[u]+cost[i];
				if(!vis[v]) vis[v]=1,cost[i]<0?q.push_front(v):q.push_back(v);
			}
		}
	}
	return dis[t]<Inf;
}

int dfs(int u,int flow) {
	if(u==t) return flow;
	int ret=0;vis[u]=1;
	for(int &i=cur[u],v;v=to[i],i;i=nxt[i])
		if(ww[i]&&dis[v]==dis[u]+cost[i]&&!vis[v]) {
			int d=dfs(v,min(flow,ww[i]));
			ww[i]-=d,ww[i^1]+=d,ret+=d,flow-=d;ans+=1ll*cost[i]*d;
			if(!flow) { vis[u]=0;break; }
		}
	return ret;
}

int n;

int main() {
	cin>>n;t=10*n+5;
	for(int i=1;i<=n;i++) {
		int x=gi(),y=gi(),z=gi();
		adde(s,i+4,z,0);
		adde(i+4,i+n+4,z,x+y);
		adde(i+4,i+2*n+4,z,x-y);
		adde(i+4,i+3*n+4,z,y-x);
		adde(i+4,i+4*n+4,z,-x-y);
		for(int j=1;j<=4;j++) adde(i+j*n+4,j,z,0);
	}
	for(int i=1;i<=n;i++) {
		int x=gi(),y=gi(),z=gi();
		adde(i+9*n+4,t,z,0);
		adde(i+5*n+4,i+9*n+4,z,x+y);
		adde(i+6*n+4,i+9*n+4,z,x-y);
		adde(i+7*n+4,i+9*n+4,z,y-x);
		adde(i+8*n+4,i+9*n+4,z,-x-y);
		for(int j=1;j<=4;j++) adde(5-j,i+(j+4)*n+4,z,0);
	}
	
	while(spfa()) memcpy(cur,h,sizeof(h)),dfs(s,inf);
	cout<<-ans;
	return 0;
}

### Prompt

Please formulate 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;
const int N=1e5+10;
typedef long long ll;
const int inf=1e9;
const ll Inf=1e18;

int gi() {
	int x=0,o=1;char ch=getchar();
	while((ch<'0'||ch>'9')&&ch!='-') ch=getchar();
	if(ch=='-') o=-1,ch=getchar();
	while(ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar();
	return x*o;
}

int to[N<<1],ww[N<<1],cost[N<<1],nxt[N<<1],tt=1,h[N],s,t,cur[N];
ll dis[N],ans=0;
bool vis[N];

void adde(int u,int v,int w,int c) {
	to[++tt]=v,ww[tt]=w,cost[tt]=c,nxt[tt]=h[u],h[u]=tt;
	to[++tt]=u,ww[tt]=0,cost[tt]=-c,nxt[tt]=h[v],h[v]=tt;
}

bool spfa() {
	memset(dis,0x3f,sizeof(dis));
	memset(vis,0,sizeof(vis));
	deque<int> q;q.push_back(s);dis[s]=0;
	while(!q.empty()) {
		int u=q.front();q.pop_front();vis[u]=0;
		for(int i=h[u],v;v=to[i],i;i=nxt[i]) {
			if(ww[i]&&dis[v]>dis[u]+cost[i]) {
				dis[v]=dis[u]+cost[i];
				if(!vis[v]) vis[v]=1,cost[i]<0?q.push_front(v):q.push_back(v);
			}
		}
	}
	return dis[t]<Inf;
}

int dfs(int u,int flow) {
	if(u==t) return flow;
	int ret=0;vis[u]=1;
	for(int &i=cur[u],v;v=to[i],i;i=nxt[i])
		if(ww[i]&&dis[v]==dis[u]+cost[i]&&!vis[v]) {
			int d=dfs(v,min(flow,ww[i]));
			ww[i]-=d,ww[i^1]+=d,ret+=d,flow-=d;ans+=1ll*cost[i]*d;
			if(!flow) { vis[u]=0;break; }
		}
	return ret;
}

int n;

int main() {
	cin>>n;t=10*n+5;
	for(int i=1;i<=n;i++) {
		int x=gi(),y=gi(),z=gi();
		adde(s,i+4,z,0);
		adde(i+4,i+n+4,z,x+y);
		adde(i+4,i+2*n+4,z,x-y);
		adde(i+4,i+3*n+4,z,y-x);
		adde(i+4,i+4*n+4,z,-x-y);
		for(int j=1;j<=4;j++) adde(i+j*n+4,j,z,0);
	}
	for(int i=1;i<=n;i++) {
		int x=gi(),y=gi(),z=gi();
		adde(i+9*n+4,t,z,0);
		adde(i+5*n+4,i+9*n+4,z,x+y);
		adde(i+6*n+4,i+9*n+4,z,x-y);
		adde(i+7*n+4,i+9*n+4,z,y-x);
		adde(i+8*n+4,i+9*n+4,z,-x-y);
		for(int j=1;j<=4;j++) adde(5-j,i+(j+4)*n+4,z,0);
	}
	
	while(spfa()) memcpy(cur,h,sizeof(h)),dfs(s,inf);
	cout<<-ans;
	return 0;
}

```