#include <bits/stdc++.h>

typedef long long LL;
typedef unsigned long long ULL;

#define debug printf("fuck %d\n", __LINE__);

inline LL read() {
	LL res = 0, bo = 1; char ch = getchar();
	while(ch < '0' || ch > '9') { if (ch == '-') bo = -1; ch = getchar(); }
	while(ch >= '0' && ch <= '9') { res = (res << 1) + (res << 3) + ch - '0'; ch = getchar(); }
	return bo * res;
}

template<typename T> void read(T &x) { x = read(); }
template<typename T, typename ...Argv> void read(T &a, Argv &...argv) { read(a); read(argv...); }

const int N = 2e5, inf = 2147483647;

struct Edge {
	int to, cap, dis;
	Edge *nxt, *pre;
	Edge(int to, int cap, int dis, Edge *nxt) : to(to), cap(cap), dis(dis), nxt(nxt), pre(NULL) {}
} *head[N], *cur[N];

LL cost, dis[N];
int S, T, flow;
bool vis[N];

void add(int u, int v, int c, int d) {
	head[u] = new Edge(v, c, d, head[u]);
	head[v] = new Edge(u, 0, -d, head[v]);
	head[u]->pre = head[v];
	head[v]->pre = head[u];
}

std::queue<int> q;

bool spfa() {
	for(int i = 1; i <= T; ++ i) dis[i] = -inf, cur[i] = head[i], vis[i] = false;
	dis[S] = 0; q.push(S);
	while (q.size()) {
		int x = q.front(); q.pop(); vis[x] = false;
		for (Edge *i = head[x]; i; i = i->nxt) {
			if (i->cap && dis[x] + i->dis > dis[i->to]) {
				dis[i->to] = dis[x] + i->dis;
				if (!vis[i->to]) q.push(i->to), vis[i->to] = true; 
			}
		}
	}
	return dis[T] != -inf;
}

int dfs(int x, int flow) {
	vis[x] = true;
	if(x == T || !flow) return flow;
	int king = 0;
	for(Edge *&i = cur[x]; i; i = i->nxt) {
		if((vis[i->to] == false || i->to == T) && i->cap && dis[x] + i->dis == dis[i->to]) {
			int o = dfs(i->to, std::min(i->cap, flow));
			if(o) {
				i->cap -= o, i->pre->cap += o;
				cost += 1LL * i->dis * o; flow -= o; king += o;
				if(!flow) return king;
			}
		}
	}
	return king;
}

void zkw_Mincost_Maxflow() {
	while(spfa()) {
		flow += dfs(S, inf);
		while(vis[T] == true) {
			for(int i = 1; i <= T; ++i) vis[i] = false;
			flow += dfs(S, inf);
		}
	}
}

int n, x, y, c, a[4];

int main() {
	read(n); S = n * 2 + 5; T = n * 2 + 6;
	for (int i = 0; i < 4; ++ i) a[i] = n * 2 + i + 1;
	for (int i = 1; i <= n; ++ i) {
		read(x, y, c);
		add(S, i, c, 0);
		add(i, a[0], inf, -x - y);
		add(i, a[1], inf, x - y);
		add(i, a[2], inf, -x + y);
		add(i, a[3], inf, x + y);
	}
	for (int i = 1; i <= n; ++ i) {
		read(x, y, c);
		add(i + n, T, c, 0);
		add(a[0], i + n, inf, x + y);
		add(a[1], i + n, inf, -x + y);
		add(a[2], i + n, inf, x - y);
		add(a[3], i + n, inf, -x - y);
	}
	zkw_Mincost_Maxflow();
	std::cout << cost << std::endl;
	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>

typedef long long LL;
typedef unsigned long long ULL;

#define debug printf("fuck %d\n", __LINE__);

inline LL read() {
	LL res = 0, bo = 1; char ch = getchar();
	while(ch < '0' || ch > '9') { if (ch == '-') bo = -1; ch = getchar(); }
	while(ch >= '0' && ch <= '9') { res = (res << 1) + (res << 3) + ch - '0'; ch = getchar(); }
	return bo * res;
}

template<typename T> void read(T &x) { x = read(); }
template<typename T, typename ...Argv> void read(T &a, Argv &...argv) { read(a); read(argv...); }

const int N = 2e5, inf = 2147483647;

struct Edge {
	int to, cap, dis;
	Edge *nxt, *pre;
	Edge(int to, int cap, int dis, Edge *nxt) : to(to), cap(cap), dis(dis), nxt(nxt), pre(NULL) {}
} *head[N], *cur[N];

LL cost, dis[N];
int S, T, flow;
bool vis[N];

void add(int u, int v, int c, int d) {
	head[u] = new Edge(v, c, d, head[u]);
	head[v] = new Edge(u, 0, -d, head[v]);
	head[u]->pre = head[v];
	head[v]->pre = head[u];
}

std::queue<int> q;

bool spfa() {
	for(int i = 1; i <= T; ++ i) dis[i] = -inf, cur[i] = head[i], vis[i] = false;
	dis[S] = 0; q.push(S);
	while (q.size()) {
		int x = q.front(); q.pop(); vis[x] = false;
		for (Edge *i = head[x]; i; i = i->nxt) {
			if (i->cap && dis[x] + i->dis > dis[i->to]) {
				dis[i->to] = dis[x] + i->dis;
				if (!vis[i->to]) q.push(i->to), vis[i->to] = true; 
			}
		}
	}
	return dis[T] != -inf;
}

int dfs(int x, int flow) {
	vis[x] = true;
	if(x == T || !flow) return flow;
	int king = 0;
	for(Edge *&i = cur[x]; i; i = i->nxt) {
		if((vis[i->to] == false || i->to == T) && i->cap && dis[x] + i->dis == dis[i->to]) {
			int o = dfs(i->to, std::min(i->cap, flow));
			if(o) {
				i->cap -= o, i->pre->cap += o;
				cost += 1LL * i->dis * o; flow -= o; king += o;
				if(!flow) return king;
			}
		}
	}
	return king;
}

void zkw_Mincost_Maxflow() {
	while(spfa()) {
		flow += dfs(S, inf);
		while(vis[T] == true) {
			for(int i = 1; i <= T; ++i) vis[i] = false;
			flow += dfs(S, inf);
		}
	}
}

int n, x, y, c, a[4];

int main() {
	read(n); S = n * 2 + 5; T = n * 2 + 6;
	for (int i = 0; i < 4; ++ i) a[i] = n * 2 + i + 1;
	for (int i = 1; i <= n; ++ i) {
		read(x, y, c);
		add(S, i, c, 0);
		add(i, a[0], inf, -x - y);
		add(i, a[1], inf, x - y);
		add(i, a[2], inf, -x + y);
		add(i, a[3], inf, x + y);
	}
	for (int i = 1; i <= n; ++ i) {
		read(x, y, c);
		add(i + n, T, c, 0);
		add(a[0], i + n, inf, x + y);
		add(a[1], i + n, inf, -x + y);
		add(a[2], i + n, inf, x - y);
		add(a[3], i + n, inf, -x - y);
	}
	zkw_Mincost_Maxflow();
	std::cout << cost << std::endl;
	return 0;
}
```