#include <bits/stdc++.h>
using namespace std;

typedef long long ll;

const ll LLINF = 4e18;
const int INF = 1e9;
const ll SHIFT = 2.01e9;

const int MAXK = 1010;
int K;

const int MAXN = 2 * MAXK;
int N, M;
int S, T;

struct edge {
	int nxt, rev, cap; ll dist;
	edge() {}
	edge(int nxt_, int rev_, int cap_, ll dist_) : nxt(nxt_), rev(rev_), cap(cap_), dist(dist_) { }
};

vector<edge> adj[MAXN];

void add_edge(int a, int b, int c, ll d) {
	assert(d >= 0);
	adj[a].push_back(edge(b, int(adj[b].size()), c, d));
	adj[b].push_back(edge(a, int(adj[a].size()) - 1, 0, -d));
}

bool vis[MAXN];
ll dist[MAXN];
int ptr[MAXN];

bool reach() {
	vector<int> q;
	q.push_back(S);
	fill_n(dist, N, LLINF);
	fill_n(vis, N, false);
	dist[S] = 0;
	for (size_t i = 0; i < q.size(); i++) {
		int cur = q[i]; vis[cur] = false;
		for (size_t j = 0; j < adj[cur].size(); j++) {
			edge& e = adj[cur][j];
			if (!e.cap || dist[e.nxt] <= dist[cur] + e.dist) {
				continue;
			}
			dist[e.nxt] = dist[cur] + e.dist;
			if (!vis[e.nxt]) {
				vis[e.nxt] = true;
				q.push_back(e.nxt);
			}
		}
	}
	return dist[T] != LLINF;
}

int dfs(int cur, int rem) {
	if (cur == T) {
		return rem;
	}
	int tot = 0;
	vis[cur] = true;
	for (int& i = ptr[cur]; i < int(adj[cur].size()); i++) {
		edge& e = adj[cur][i];
		if (!e.cap || vis[e.nxt] || dist[e.nxt] != dist[cur] + e.dist) {
			continue;
		}
		ll d = dfs(e.nxt, min(rem - tot, e.cap));
		tot += d;
		e.cap -= d;
		adj[e.nxt][e.rev].cap += d;
		if (tot == rem) {
			vis[cur] = false;
			break;
		}
	}
	return tot;
}

ll mcf(int rem = INF) {
	int totflow = 0; ll totcost = 0;
	while (reach()) {
		fill_n(ptr, N, 0);
		int d = dfs(S, rem - totflow);
		totflow += d;
		totcost += d * dist[T];
	}
	assert(totflow == rem);
	return totcost;
}

int main() {
	scanf("%d", &K);
	S = 0, T = 1;
	N = 2 * K + 6;
	int tot = 0;
	for (int i = 0; i < K; i++) {
		ll x, y; int c; scanf("%lld %lld %d", &x, &y, &c);
		tot += c;
		add_edge(S, 6+i, c, 0);
		add_edge(6+i, 2, INF, -(x + y) + SHIFT);
		add_edge(6+i, 3, INF, -(x - y) + SHIFT);
		add_edge(6+i, 4, INF, -(-x + y) + SHIFT);
		add_edge(6+i, 5, INF, -(-x - y) + SHIFT);
	}
	for (int i = 0; i < K; i++) {
		ll x, y; int c; scanf("%lld %lld %d", &x, &y, &c);
		add_edge(6+K+i, T, c, 0);
		add_edge(2, 6+K+i, INF, -(-x - y) + SHIFT);
		add_edge(3, 6+K+i, INF, -(-x + y) + SHIFT);
		add_edge(4, 6+K+i, INF, -(x - y) + SHIFT);
		add_edge(5, 6+K+i, INF, -(x + y) + SHIFT);
	}

	cerr << "tot = " << tot << endl;

	ll ans = -mcf(tot) + 2 * tot * SHIFT;
	printf("%lld\n", ans);

	return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

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;

typedef long long ll;

const ll LLINF = 4e18;
const int INF = 1e9;
const ll SHIFT = 2.01e9;

const int MAXK = 1010;
int K;

const int MAXN = 2 * MAXK;
int N, M;
int S, T;

struct edge {
	int nxt, rev, cap; ll dist;
	edge() {}
	edge(int nxt_, int rev_, int cap_, ll dist_) : nxt(nxt_), rev(rev_), cap(cap_), dist(dist_) { }
};

vector<edge> adj[MAXN];

void add_edge(int a, int b, int c, ll d) {
	assert(d >= 0);
	adj[a].push_back(edge(b, int(adj[b].size()), c, d));
	adj[b].push_back(edge(a, int(adj[a].size()) - 1, 0, -d));
}

bool vis[MAXN];
ll dist[MAXN];
int ptr[MAXN];

bool reach() {
	vector<int> q;
	q.push_back(S);
	fill_n(dist, N, LLINF);
	fill_n(vis, N, false);
	dist[S] = 0;
	for (size_t i = 0; i < q.size(); i++) {
		int cur = q[i]; vis[cur] = false;
		for (size_t j = 0; j < adj[cur].size(); j++) {
			edge& e = adj[cur][j];
			if (!e.cap || dist[e.nxt] <= dist[cur] + e.dist) {
				continue;
			}
			dist[e.nxt] = dist[cur] + e.dist;
			if (!vis[e.nxt]) {
				vis[e.nxt] = true;
				q.push_back(e.nxt);
			}
		}
	}
	return dist[T] != LLINF;
}

int dfs(int cur, int rem) {
	if (cur == T) {
		return rem;
	}
	int tot = 0;
	vis[cur] = true;
	for (int& i = ptr[cur]; i < int(adj[cur].size()); i++) {
		edge& e = adj[cur][i];
		if (!e.cap || vis[e.nxt] || dist[e.nxt] != dist[cur] + e.dist) {
			continue;
		}
		ll d = dfs(e.nxt, min(rem - tot, e.cap));
		tot += d;
		e.cap -= d;
		adj[e.nxt][e.rev].cap += d;
		if (tot == rem) {
			vis[cur] = false;
			break;
		}
	}
	return tot;
}

ll mcf(int rem = INF) {
	int totflow = 0; ll totcost = 0;
	while (reach()) {
		fill_n(ptr, N, 0);
		int d = dfs(S, rem - totflow);
		totflow += d;
		totcost += d * dist[T];
	}
	assert(totflow == rem);
	return totcost;
}

int main() {
	scanf("%d", &K);
	S = 0, T = 1;
	N = 2 * K + 6;
	int tot = 0;
	for (int i = 0; i < K; i++) {
		ll x, y; int c; scanf("%lld %lld %d", &x, &y, &c);
		tot += c;
		add_edge(S, 6+i, c, 0);
		add_edge(6+i, 2, INF, -(x + y) + SHIFT);
		add_edge(6+i, 3, INF, -(x - y) + SHIFT);
		add_edge(6+i, 4, INF, -(-x + y) + SHIFT);
		add_edge(6+i, 5, INF, -(-x - y) + SHIFT);
	}
	for (int i = 0; i < K; i++) {
		ll x, y; int c; scanf("%lld %lld %d", &x, &y, &c);
		add_edge(6+K+i, T, c, 0);
		add_edge(2, 6+K+i, INF, -(-x - y) + SHIFT);
		add_edge(3, 6+K+i, INF, -(-x + y) + SHIFT);
		add_edge(4, 6+K+i, INF, -(x - y) + SHIFT);
		add_edge(5, 6+K+i, INF, -(x + y) + SHIFT);
	}

	cerr << "tot = " << tot << endl;

	ll ans = -mcf(tot) + 2 * tot * SHIFT;
	printf("%lld\n", ans);

	return 0;
}

```