#include <bits/stdc++.h>

typedef long long int int64;
static const int64 MAX = 2000000001LL;
struct vertex {
	int estart;
	int64 dist,ldist;
	int frome;
} v[4003];
struct edge {
	int enext,to;
	int cap;
	int64 cost;
} e[20003];int en;
void addedge(int a,int b,int cap,int64 cost)
{
	e[en].enext = v[a].estart;e[en].to = b;e[en].cap = cap;e[en].cost = cost;v[a].estart = en++;
	e[en].enext = v[b].estart;e[en].to = a;e[en].cap = 0;e[en].cost = -cost;v[b].estart = en++;
}
int n;
int main()
{
	scanf("%d",&n);
	for(int i = 0;i < 6+n+n;++i) {
		v[i].estart = -1;
	}
	for(int i = 6+n;i < 6+n+n;++i) {
		v[i].dist = -4*MAX;
	}
	for(int i = 2;i < 6;++i) {
		v[i].dist = -2*MAX;
	}
	v[1].dist = -4*MAX;
	// 6+n+n
	for(int i = 0;i < n;++i) {
		int64 x,y;int k;
		scanf("%lld%lld%d",&x,&y,&k);
		addedge(0,6+i,k,0);
		addedge(6+i,2,k,x+y); // inf
		addedge(6+i,3,k,x-y);
		addedge(6+i,4,k,-x+y);
		addedge(6+i,5,k,-x-y);
	}
	for(int i = 0;i < n;++i) {
		int64 x,y;int k;
		scanf("%lld%lld%d",&x,&y,&k);
		addedge(6+n+i,1,k,0);
		addedge(2,6+n+i,k,-x-y);
		addedge(3,6+n+i,k,-x+y);
		addedge(4,6+n+i,k,x-y);
		addedge(5,6+n+i,k,x+y);
	}
	int64 cost = 0;
	int flow = 0;
	for(;;) {
		for(int i = 0;i < 6+n+n;++i) {
			v[i].ldist = v[i].dist;
			v[i].dist = -1;
		}
		v[0].dist = 0;
		using pair = std::pair<int64,int>;
		std::priority_queue<pair,std::vector<pair>,std::greater<pair> > pq;
		pq.push(std::make_pair(v[0].dist-v[0].ldist,0));
		while(!pq.empty()) {
			pair curp = pq.top();pq.pop();
			int cur = curp.second;
			int64 dist = curp.first+v[cur].ldist;
			if(v[cur].dist != dist) continue;
			for(int j = v[cur].estart;j != -1;j = e[j].enext) {
				if(e[j].cap == 0) continue;
				int to = e[j].to;
				if(v[to].dist == -1 || v[to].dist > dist+e[j].cost) {
					v[to].dist = dist+e[j].cost;
					v[to].frome = j;
					pq.push(std::make_pair(v[to].dist-v[to].ldist,to));
					assert(v[to].dist-v[to].ldist>=v[cur].dist-v[cur].ldist);
				}
			}
		}
		if(v[1].dist == -1) break;
		int cnt = 99999;
		for(int j = 1;j != 0;j = e[v[j].frome^1].to) {
			int k = v[j].frome;
			if(e[k].cap < cnt) cnt = e[k].cap;
		}
		for(int j = 1;j != 0;j = e[v[j].frome^1].to) {
			int k = v[j].frome;
			e[k].cap -= cnt;
			e[k^1].cap += cnt;
		}
		cost += v[1].dist * cnt;
		flow += cnt;
	}
	printf("%lld\n", -cost);
}

### Prompt

Create a solution in cpp for 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>

typedef long long int int64;
static const int64 MAX = 2000000001LL;
struct vertex {
	int estart;
	int64 dist,ldist;
	int frome;
} v[4003];
struct edge {
	int enext,to;
	int cap;
	int64 cost;
} e[20003];int en;
void addedge(int a,int b,int cap,int64 cost)
{
	e[en].enext = v[a].estart;e[en].to = b;e[en].cap = cap;e[en].cost = cost;v[a].estart = en++;
	e[en].enext = v[b].estart;e[en].to = a;e[en].cap = 0;e[en].cost = -cost;v[b].estart = en++;
}
int n;
int main()
{
	scanf("%d",&n);
	for(int i = 0;i < 6+n+n;++i) {
		v[i].estart = -1;
	}
	for(int i = 6+n;i < 6+n+n;++i) {
		v[i].dist = -4*MAX;
	}
	for(int i = 2;i < 6;++i) {
		v[i].dist = -2*MAX;
	}
	v[1].dist = -4*MAX;
	// 6+n+n
	for(int i = 0;i < n;++i) {
		int64 x,y;int k;
		scanf("%lld%lld%d",&x,&y,&k);
		addedge(0,6+i,k,0);
		addedge(6+i,2,k,x+y); // inf
		addedge(6+i,3,k,x-y);
		addedge(6+i,4,k,-x+y);
		addedge(6+i,5,k,-x-y);
	}
	for(int i = 0;i < n;++i) {
		int64 x,y;int k;
		scanf("%lld%lld%d",&x,&y,&k);
		addedge(6+n+i,1,k,0);
		addedge(2,6+n+i,k,-x-y);
		addedge(3,6+n+i,k,-x+y);
		addedge(4,6+n+i,k,x-y);
		addedge(5,6+n+i,k,x+y);
	}
	int64 cost = 0;
	int flow = 0;
	for(;;) {
		for(int i = 0;i < 6+n+n;++i) {
			v[i].ldist = v[i].dist;
			v[i].dist = -1;
		}
		v[0].dist = 0;
		using pair = std::pair<int64,int>;
		std::priority_queue<pair,std::vector<pair>,std::greater<pair> > pq;
		pq.push(std::make_pair(v[0].dist-v[0].ldist,0));
		while(!pq.empty()) {
			pair curp = pq.top();pq.pop();
			int cur = curp.second;
			int64 dist = curp.first+v[cur].ldist;
			if(v[cur].dist != dist) continue;
			for(int j = v[cur].estart;j != -1;j = e[j].enext) {
				if(e[j].cap == 0) continue;
				int to = e[j].to;
				if(v[to].dist == -1 || v[to].dist > dist+e[j].cost) {
					v[to].dist = dist+e[j].cost;
					v[to].frome = j;
					pq.push(std::make_pair(v[to].dist-v[to].ldist,to));
					assert(v[to].dist-v[to].ldist>=v[cur].dist-v[cur].ldist);
				}
			}
		}
		if(v[1].dist == -1) break;
		int cnt = 99999;
		for(int j = 1;j != 0;j = e[v[j].frome^1].to) {
			int k = v[j].frome;
			if(e[k].cap < cnt) cnt = e[k].cap;
		}
		for(int j = 1;j != 0;j = e[v[j].frome^1].to) {
			int k = v[j].frome;
			e[k].cap -= cnt;
			e[k^1].cap += cnt;
		}
		cost += v[1].dist * cnt;
		flow += cnt;
	}
	printf("%lld\n", -cost);
}

```