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

const int inf = 10, maxn = 1e5;

int ans;

namespace MCMF{
	int head[maxn], nxt[maxn], to[maxn], c[maxn], r[maxn], tot = 1;
	void add(int u, int v, int w, int f) {
		assert(++tot < maxn);
		nxt[tot] = head[u];
		to[tot] = v;
		c[tot] = w;
		r[tot] = f;
		head[u] = tot;
	}
	void add2(int u, int v, int w, int f) {
		add(u,v,w,f), add(v,u,-w,0);
	}
#define mp make_pair
	typedef pair<long long, int> qnode;
	int dis[maxn], inq[maxn], pre[maxn];
	void spfa(int s) {
		memset(dis, 0x3f, sizeof(dis));
		memset(pre, 0, sizeof(pre));
		queue<int> q;
		dis[s] = 0;
		q.push(s);
		while (!q.empty()) {
			int u = q.front();
			q.pop(); inq[u] = 0;
			for (int e = head[u]; e; e = nxt[e]) {
				if (!r[e]) continue;
				int v = to[e], w = c[e];
				if (dis[u]+w < dis[v]) {
					pre[v] = e;
					dis[v] = dis[u]+w;
					if (!inq[v]) {
						q.push(v);
						inq[v] = 1;
					}
				}
			}
		}
	}
	void augment(int t) {
		int flow = inf;
		for (int e = pre[t]; e; e = pre[to[e^1]]) {
			flow = min(flow, r[e]);
		}
		for (int e = pre[t]; e; e = pre[to[e^1]]) {
			r[e] -= flow;
			r[e^1] += flow;
		}
		ans += flow*dis[t];
	}
}
using namespace MCMF;


int n, rx[maxn], ry[maxn], rc[maxn], bx[maxn], by[maxn], bc[maxn];
signed main() {
	cin >> n;
	for (int i = 0; i < n; ++i) {
		cin >> rx[i] >> ry[i] >> rc[i];
		add2(1, i+10, 0, rc[i]);
		add2(i+10, 3, rx[i]+ry[i], inf);
		add2(i+10, 4, rx[i]-ry[i], inf);
		add2(i+10, 5, -rx[i]+ry[i], inf);
		add2(i+10, 6, -rx[i]-ry[i], inf);
	}
	for (int i = n; i < 2*n; ++i) {
		cin >> bx[i] >> by[i] >> bc[i];
		add2(3, i+10, -bx[i]-by[i], inf);
		add2(4, i+10, -bx[i]+by[i], inf);
		add2(5, i+10, bx[i]-by[i], inf);
		add2(6, i+10, bx[i]+by[i], inf);
		add2(i+10, 2, 0, bc[i]);
	}
	while (spfa(1), pre[2]) augment(2);
	cout << -ans;
}
### Prompt

Please provide a CPP coded solution 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>
#define int long long
using namespace std;

const int inf = 10, maxn = 1e5;

int ans;

namespace MCMF{
	int head[maxn], nxt[maxn], to[maxn], c[maxn], r[maxn], tot = 1;
	void add(int u, int v, int w, int f) {
		assert(++tot < maxn);
		nxt[tot] = head[u];
		to[tot] = v;
		c[tot] = w;
		r[tot] = f;
		head[u] = tot;
	}
	void add2(int u, int v, int w, int f) {
		add(u,v,w,f), add(v,u,-w,0);
	}
#define mp make_pair
	typedef pair<long long, int> qnode;
	int dis[maxn], inq[maxn], pre[maxn];
	void spfa(int s) {
		memset(dis, 0x3f, sizeof(dis));
		memset(pre, 0, sizeof(pre));
		queue<int> q;
		dis[s] = 0;
		q.push(s);
		while (!q.empty()) {
			int u = q.front();
			q.pop(); inq[u] = 0;
			for (int e = head[u]; e; e = nxt[e]) {
				if (!r[e]) continue;
				int v = to[e], w = c[e];
				if (dis[u]+w < dis[v]) {
					pre[v] = e;
					dis[v] = dis[u]+w;
					if (!inq[v]) {
						q.push(v);
						inq[v] = 1;
					}
				}
			}
		}
	}
	void augment(int t) {
		int flow = inf;
		for (int e = pre[t]; e; e = pre[to[e^1]]) {
			flow = min(flow, r[e]);
		}
		for (int e = pre[t]; e; e = pre[to[e^1]]) {
			r[e] -= flow;
			r[e^1] += flow;
		}
		ans += flow*dis[t];
	}
}
using namespace MCMF;


int n, rx[maxn], ry[maxn], rc[maxn], bx[maxn], by[maxn], bc[maxn];
signed main() {
	cin >> n;
	for (int i = 0; i < n; ++i) {
		cin >> rx[i] >> ry[i] >> rc[i];
		add2(1, i+10, 0, rc[i]);
		add2(i+10, 3, rx[i]+ry[i], inf);
		add2(i+10, 4, rx[i]-ry[i], inf);
		add2(i+10, 5, -rx[i]+ry[i], inf);
		add2(i+10, 6, -rx[i]-ry[i], inf);
	}
	for (int i = n; i < 2*n; ++i) {
		cin >> bx[i] >> by[i] >> bc[i];
		add2(3, i+10, -bx[i]-by[i], inf);
		add2(4, i+10, -bx[i]+by[i], inf);
		add2(5, i+10, bx[i]-by[i], inf);
		add2(6, i+10, bx[i]+by[i], inf);
		add2(i+10, 2, 0, bc[i]);
	}
	while (spfa(1), pre[2]) augment(2);
	cout << -ans;
}
```