#include <bits/stdc++.h>
#define rep(i, l, r) for (register int i = l; i <= r; i++)
#define per(i, r, l) for (register int i = r; i >= l; i--)
#define srep(i, l, r) for (register int i = l; i < r; i++)
#define sper(i, r, l) for (register int i = r; i > l; i--)
#define erep(i, x) for (register int i = h[x]; i; i = e[i].next)
#define maxn 3020
#define maxm 30020
#define ll long long int 
using namespace std;

const int inf = 2000000020;

int n, m, s, t;
struct edge{
	int next, to, flow, cost;
	edge(int next, int to, int flow, ll cost) : next(next), to(to), flow(flow), cost(cost){}
	edge(){}
}e[maxm << 1];
int cnt = 1, h[maxn];
void Add_Edge(int x, int y, int z, ll w){
	e[++cnt] = edge(h[x], y, z, w);
	h[x] = cnt;
	e[++cnt] = edge(h[y], x, 0, -w);
	h[y] = cnt;
}
int p[maxn];
ll d[maxn];
bool und[maxn];
int spfa[maxn];
bool vis[maxn];
int head = 0, tail = 0;
bool SPFA(){
	rep(i, s, t) und[i] = 1;
	d[s] = 0, und[s] = 0;
	head = tail = 0;
	spfa[++head] = s;
	vis[s] = 1;
	while (head != tail){
		int x = spfa[++tail];
		tail = (tail == maxn - 1) ? 0 : tail;
		erep(i, x){
			if (!e[i].flow) continue;
			int op = e[i].to;
			if (d[op] > d[x] + e[i].cost || und[op]){
				p[op] = i;
				und[op] = 0;
				d[op] = d[x] + e[i].cost;
				if (!vis[op]) {
					vis[op] = 1;
					spfa[++head] = op;
					head = (head == maxn - 1) ? 0 : head;
				}
			}
		}
		vis[x] = 0;
	}
	return !und[t];
}
void Augment(int& maxflow, ll& mincost){
	int now = t, flow = inf;
	while (now != s){
		int k = p[now];
		flow = min(flow, e[k].flow);
		now = e[k ^ 1].to;
	}
	now = t;
	while (now != s){
		int k = p[now];
		e[k].flow -= flow, e[k ^ 1].flow += flow;
		now = e[k ^ 1].to;
	}
	maxflow += flow, mincost += (d[t] - d[s]) * flow;
}
void MCMF(int& maxflow, ll& mincost){
	while (SPFA()) Augment(maxflow, mincost);
}
//     R      B
// 1  + +    - -
// 2  + -    - +
// 3  - +    + -
// 4  - -    + +

int main(){
	int T, sum = 0;
	ll x, y, z;
	scanf("%d", &T);
	s = 0, t = 2 * T + 5;
	rep(TT, 1, T){ //4 + TT
		scanf("%lld%lld%lld", &x, &y, &z);
		Add_Edge(s, 4 + TT, z, 0);
		Add_Edge(4 + TT, 1, z, -(+ x + y));
		Add_Edge(4 + TT, 2, z, -(+ x - y));
		Add_Edge(4 + TT, 3, z, -(- x + y));
		Add_Edge(4 + TT, 4, z, -(- x - y));
		sum += z;
	}
	rep(TT, 1, T){ //4 + TT + T
		scanf("%lld%lld%lld", &x, &y, &z);
		Add_Edge(4 + TT + T, t, z, 0);
		Add_Edge(1, 4 + TT + T, z, +(+ x + y));
		Add_Edge(2, 4 + TT + T, z, +(+ x - y));
		Add_Edge(3, 4 + TT + T, z, +(- x + y));
		Add_Edge(4, 4 + TT + T, z, +(- x - y));
	}
	int maxflow = 0;
	ll mincost = 0;
	MCMF(maxflow, mincost);
	assert(maxflow == sum);
	printf("%lld\n", -mincost);
	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>
#define rep(i, l, r) for (register int i = l; i <= r; i++)
#define per(i, r, l) for (register int i = r; i >= l; i--)
#define srep(i, l, r) for (register int i = l; i < r; i++)
#define sper(i, r, l) for (register int i = r; i > l; i--)
#define erep(i, x) for (register int i = h[x]; i; i = e[i].next)
#define maxn 3020
#define maxm 30020
#define ll long long int 
using namespace std;

const int inf = 2000000020;

int n, m, s, t;
struct edge{
	int next, to, flow, cost;
	edge(int next, int to, int flow, ll cost) : next(next), to(to), flow(flow), cost(cost){}
	edge(){}
}e[maxm << 1];
int cnt = 1, h[maxn];
void Add_Edge(int x, int y, int z, ll w){
	e[++cnt] = edge(h[x], y, z, w);
	h[x] = cnt;
	e[++cnt] = edge(h[y], x, 0, -w);
	h[y] = cnt;
}
int p[maxn];
ll d[maxn];
bool und[maxn];
int spfa[maxn];
bool vis[maxn];
int head = 0, tail = 0;
bool SPFA(){
	rep(i, s, t) und[i] = 1;
	d[s] = 0, und[s] = 0;
	head = tail = 0;
	spfa[++head] = s;
	vis[s] = 1;
	while (head != tail){
		int x = spfa[++tail];
		tail = (tail == maxn - 1) ? 0 : tail;
		erep(i, x){
			if (!e[i].flow) continue;
			int op = e[i].to;
			if (d[op] > d[x] + e[i].cost || und[op]){
				p[op] = i;
				und[op] = 0;
				d[op] = d[x] + e[i].cost;
				if (!vis[op]) {
					vis[op] = 1;
					spfa[++head] = op;
					head = (head == maxn - 1) ? 0 : head;
				}
			}
		}
		vis[x] = 0;
	}
	return !und[t];
}
void Augment(int& maxflow, ll& mincost){
	int now = t, flow = inf;
	while (now != s){
		int k = p[now];
		flow = min(flow, e[k].flow);
		now = e[k ^ 1].to;
	}
	now = t;
	while (now != s){
		int k = p[now];
		e[k].flow -= flow, e[k ^ 1].flow += flow;
		now = e[k ^ 1].to;
	}
	maxflow += flow, mincost += (d[t] - d[s]) * flow;
}
void MCMF(int& maxflow, ll& mincost){
	while (SPFA()) Augment(maxflow, mincost);
}
//     R      B
// 1  + +    - -
// 2  + -    - +
// 3  - +    + -
// 4  - -    + +

int main(){
	int T, sum = 0;
	ll x, y, z;
	scanf("%d", &T);
	s = 0, t = 2 * T + 5;
	rep(TT, 1, T){ //4 + TT
		scanf("%lld%lld%lld", &x, &y, &z);
		Add_Edge(s, 4 + TT, z, 0);
		Add_Edge(4 + TT, 1, z, -(+ x + y));
		Add_Edge(4 + TT, 2, z, -(+ x - y));
		Add_Edge(4 + TT, 3, z, -(- x + y));
		Add_Edge(4 + TT, 4, z, -(- x - y));
		sum += z;
	}
	rep(TT, 1, T){ //4 + TT + T
		scanf("%lld%lld%lld", &x, &y, &z);
		Add_Edge(4 + TT + T, t, z, 0);
		Add_Edge(1, 4 + TT + T, z, +(+ x + y));
		Add_Edge(2, 4 + TT + T, z, +(+ x - y));
		Add_Edge(3, 4 + TT + T, z, +(- x + y));
		Add_Edge(4, 4 + TT + T, z, +(- x - y));
	}
	int maxflow = 0;
	ll mincost = 0;
	MCMF(maxflow, mincost);
	assert(maxflow == sum);
	printf("%lld\n", -mincost);
	return 0;
}
```