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

typedef long long ll;
const int INF32 = 1 << 30;
const ll INF64 = 1ll << 60;

const int N = 1005;
int n;

namespace flow {
	const int V = 2 * N, E = 2 * (10 * N);
	int S, T, tot = 1, nxt[E], fst[V], to[E], flow[E], cost[E], pre[V];
	ll dis[V];
	void addedge(int u, int v, int w, int c) {
		nxt[++tot] = fst[u]; fst[u] = tot; to[tot] = v; flow[tot] = w; cost[tot] = c;
		nxt[++tot] = fst[v]; fst[v] = tot; to[tot] = u; flow[tot] = 0; cost[tot] = -c;
	}
	bool bfs() {
		queue<int> q;
		static bool inq[V];
		for (int i = 1; i <= flow::T; i++) dis[i] = INF64;
		q.push(S), inq[S] = true, dis[S] = 0;
		while (!q.empty()) {
			int u = q.front(); q.pop(); inq[u] = false;
			for (int i = fst[u]; i; i = nxt[i])
				if (flow[i] > 0 && dis[to[i]] > dis[u] + cost[i]) {
					dis[to[i]] = dis[u] + cost[i];
					pre[to[i]] = i;
					if (!inq[to[i]]) q.push(to[i]), inq[to[i]] = true;
				}
		}
		return dis[T] != INF64;
	}
	pair<int, ll> mcmf() {
		int f = 0;
		ll c = 0;
		while (bfs()) {
			int mn = INF32;
			for (int i = T; i != S; i = to[pre[i] ^ 1]) mn = min(mn, flow[pre[i]]);
			f += mn, c += mn * dis[T];
			for (int i = T; i != S; i = to[pre[i] ^ 1]) flow[pre[i]] -= mn, flow[pre[i] ^ 1] += mn;
		}
		return make_pair(f, c);
	}
}

int main() {
	ios::sync_with_stdio(false), cin.tie(0);
	cin >> n;
	flow::S = 2 * n + 5, flow::T = 2 * n + 6;
	for (int i = 1, x, y, c; i <= n; ++i) {
		cin >> x >> y >> c;
		flow::addedge(flow::S, i, c, 0);
		flow::addedge(i, 2 * n + 1, INF32, +x + y);
		flow::addedge(i, 2 * n + 2, INF32, +x - y);
		flow::addedge(i, 2 * n + 3, INF32, -x + y);
		flow::addedge(i, 2 * n + 4, INF32, -x - y);
	}
	for (int i = 1, x, y, c; i <= n; ++i) {
		cin >> x >> y >> c;
		flow::addedge(i + n, flow::T, c, 0);
		flow::addedge(2 * n + 1, i + n, INF32, -x - y);
		flow::addedge(2 * n + 2, i + n, INF32, -x + y);
		flow::addedge(2 * n + 3, i + n, INF32, +x - y);
		flow::addedge(2 * n + 4, i + n, INF32, +x + y);
	}
	cout << -flow::mcmf().second << endl;
}

### 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;

typedef long long ll;
const int INF32 = 1 << 30;
const ll INF64 = 1ll << 60;

const int N = 1005;
int n;

namespace flow {
	const int V = 2 * N, E = 2 * (10 * N);
	int S, T, tot = 1, nxt[E], fst[V], to[E], flow[E], cost[E], pre[V];
	ll dis[V];
	void addedge(int u, int v, int w, int c) {
		nxt[++tot] = fst[u]; fst[u] = tot; to[tot] = v; flow[tot] = w; cost[tot] = c;
		nxt[++tot] = fst[v]; fst[v] = tot; to[tot] = u; flow[tot] = 0; cost[tot] = -c;
	}
	bool bfs() {
		queue<int> q;
		static bool inq[V];
		for (int i = 1; i <= flow::T; i++) dis[i] = INF64;
		q.push(S), inq[S] = true, dis[S] = 0;
		while (!q.empty()) {
			int u = q.front(); q.pop(); inq[u] = false;
			for (int i = fst[u]; i; i = nxt[i])
				if (flow[i] > 0 && dis[to[i]] > dis[u] + cost[i]) {
					dis[to[i]] = dis[u] + cost[i];
					pre[to[i]] = i;
					if (!inq[to[i]]) q.push(to[i]), inq[to[i]] = true;
				}
		}
		return dis[T] != INF64;
	}
	pair<int, ll> mcmf() {
		int f = 0;
		ll c = 0;
		while (bfs()) {
			int mn = INF32;
			for (int i = T; i != S; i = to[pre[i] ^ 1]) mn = min(mn, flow[pre[i]]);
			f += mn, c += mn * dis[T];
			for (int i = T; i != S; i = to[pre[i] ^ 1]) flow[pre[i]] -= mn, flow[pre[i] ^ 1] += mn;
		}
		return make_pair(f, c);
	}
}

int main() {
	ios::sync_with_stdio(false), cin.tie(0);
	cin >> n;
	flow::S = 2 * n + 5, flow::T = 2 * n + 6;
	for (int i = 1, x, y, c; i <= n; ++i) {
		cin >> x >> y >> c;
		flow::addedge(flow::S, i, c, 0);
		flow::addedge(i, 2 * n + 1, INF32, +x + y);
		flow::addedge(i, 2 * n + 2, INF32, +x - y);
		flow::addedge(i, 2 * n + 3, INF32, -x + y);
		flow::addedge(i, 2 * n + 4, INF32, -x - y);
	}
	for (int i = 1, x, y, c; i <= n; ++i) {
		cin >> x >> y >> c;
		flow::addedge(i + n, flow::T, c, 0);
		flow::addedge(2 * n + 1, i + n, INF32, -x - y);
		flow::addedge(2 * n + 2, i + n, INF32, -x + y);
		flow::addedge(2 * n + 3, i + n, INF32, +x - y);
		flow::addedge(2 * n + 4, i + n, INF32, +x + y);
	}
	cout << -flow::mcmf().second << endl;
}

```