#include <algorithm>
#include <cstring>
#include <cstdio>
using ll = long long;
int lst[3005], to[20005], pre[20005], cap[20005], cost[20005], que[2000005], tot;
ll dis[3005];
bool in[3005], vis[3005];
inline void add_edge(int u, int v, int _cap, int _cost)
{
	auto _add = [&] (int x, int y, int ca, int co)
	{
		to[tot] = y;
		pre[tot] = lst[x];
		cap[tot] = ca;
		cost[tot] = co;
		lst[x] = tot++;
	};
	_add(u, v, _cap, _cost);
	_add(v, u, 0, -_cost);
}
int dfs(int u, int t, int rem)
{
	if (u == t)
		return rem;
	vis[u] = true;
	int ans = 0;
	for (int i = lst[u]; ~i; i = pre[i])
	{
		if (vis[to[i]] || !cap[i] || dis[to[i]] != dis[u] + cost[i])
			continue;
		int v = to[i], res = dfs(v, t, std::min(rem - ans, cap[i]));
		cap[i] -= res;
		cap[i ^ 1] += res;
		ans += res;
		if (ans == rem)
			return ans;
	}
	return ans;
}
inline ll min_cost_max_flow(int s, int t)
{
	ll res = 0;
	while (true)
	{
		memset(dis, 0x3f, sizeof(dis));
		memset(in, false, sizeof(in));
		int he = 0, ta = 0;
		que[ta++] = s;
		dis[s] = 0;
		in[s] = true;
		auto update = [&] ()
		{
			if (he < ta && dis[que[he]] > dis[que[ta - 1]])
				std::swap(que[he], que[ta - 1]);
		};
		while (he < ta)
		{
			int u = que[he++];
			in[u] = false;
			update();
			for (int i = lst[u]; ~i; i = pre[i])
			{
				if (cap[i] && dis[to[i]] > dis[u] + cost[i])
				{
					dis[to[i]] = dis[u] + cost[i];
					if (!in[to[i]])
					{
						in[to[i]] = true;
						que[ta++] = to[i];
						update();
					}
				}
			}
		}
		if (dis[t] >= 1e9)
			break;
		while (true)
		{
			for (int i = 0; i < ta; i++)
				vis[que[i]] = false;
			int mn = dfs(s, t, 1e9);
			if (!mn)
				break;
			res += (ll)mn * dis[t];
		}
	}
	return res;
}
int main()
{
	// freopen("AGC034-D.in", "r", stdin);
	memset(lst, -1, sizeof(lst));
	int n;
	scanf("%d", &n);
	for (int i = 0; i < n; i++)
	{
		int x, y, k;
		scanf("%d%d%d", &x, &y, &k);
		add_edge(0, i + 1, k, 0);
		add_edge(i + 1, 2 * n + 1, k,  x + y);
		add_edge(i + 1, 2 * n + 2, k, -x + y);
		add_edge(i + 1, 2 * n + 3, k,  x - y);
		add_edge(i + 1, 2 * n + 4, k, -x - y);
	}
	for (int i = 0; i < n; i++)
	{
		int x, y, k;
		scanf("%d%d%d", &x, &y, &k);
		add_edge(n + i + 1, 2 * n + 5, k, 0);
		add_edge(2 * n + 1, n + i + 1, k, -x - y);
		add_edge(2 * n + 2, n + i + 1, k,  x - y);
		add_edge(2 * n + 3, n + i + 1, k, -x + y);
		add_edge(2 * n + 4, n + i + 1, k,  x + y);
	}
	printf("%lld\n", -min_cost_max_flow(0, 2 * n + 5));
	return 0;
}

### Prompt

In Cpp, your task is to solve 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 <algorithm>
#include <cstring>
#include <cstdio>
using ll = long long;
int lst[3005], to[20005], pre[20005], cap[20005], cost[20005], que[2000005], tot;
ll dis[3005];
bool in[3005], vis[3005];
inline void add_edge(int u, int v, int _cap, int _cost)
{
	auto _add = [&] (int x, int y, int ca, int co)
	{
		to[tot] = y;
		pre[tot] = lst[x];
		cap[tot] = ca;
		cost[tot] = co;
		lst[x] = tot++;
	};
	_add(u, v, _cap, _cost);
	_add(v, u, 0, -_cost);
}
int dfs(int u, int t, int rem)
{
	if (u == t)
		return rem;
	vis[u] = true;
	int ans = 0;
	for (int i = lst[u]; ~i; i = pre[i])
	{
		if (vis[to[i]] || !cap[i] || dis[to[i]] != dis[u] + cost[i])
			continue;
		int v = to[i], res = dfs(v, t, std::min(rem - ans, cap[i]));
		cap[i] -= res;
		cap[i ^ 1] += res;
		ans += res;
		if (ans == rem)
			return ans;
	}
	return ans;
}
inline ll min_cost_max_flow(int s, int t)
{
	ll res = 0;
	while (true)
	{
		memset(dis, 0x3f, sizeof(dis));
		memset(in, false, sizeof(in));
		int he = 0, ta = 0;
		que[ta++] = s;
		dis[s] = 0;
		in[s] = true;
		auto update = [&] ()
		{
			if (he < ta && dis[que[he]] > dis[que[ta - 1]])
				std::swap(que[he], que[ta - 1]);
		};
		while (he < ta)
		{
			int u = que[he++];
			in[u] = false;
			update();
			for (int i = lst[u]; ~i; i = pre[i])
			{
				if (cap[i] && dis[to[i]] > dis[u] + cost[i])
				{
					dis[to[i]] = dis[u] + cost[i];
					if (!in[to[i]])
					{
						in[to[i]] = true;
						que[ta++] = to[i];
						update();
					}
				}
			}
		}
		if (dis[t] >= 1e9)
			break;
		while (true)
		{
			for (int i = 0; i < ta; i++)
				vis[que[i]] = false;
			int mn = dfs(s, t, 1e9);
			if (!mn)
				break;
			res += (ll)mn * dis[t];
		}
	}
	return res;
}
int main()
{
	// freopen("AGC034-D.in", "r", stdin);
	memset(lst, -1, sizeof(lst));
	int n;
	scanf("%d", &n);
	for (int i = 0; i < n; i++)
	{
		int x, y, k;
		scanf("%d%d%d", &x, &y, &k);
		add_edge(0, i + 1, k, 0);
		add_edge(i + 1, 2 * n + 1, k,  x + y);
		add_edge(i + 1, 2 * n + 2, k, -x + y);
		add_edge(i + 1, 2 * n + 3, k,  x - y);
		add_edge(i + 1, 2 * n + 4, k, -x - y);
	}
	for (int i = 0; i < n; i++)
	{
		int x, y, k;
		scanf("%d%d%d", &x, &y, &k);
		add_edge(n + i + 1, 2 * n + 5, k, 0);
		add_edge(2 * n + 1, n + i + 1, k, -x - y);
		add_edge(2 * n + 2, n + i + 1, k,  x - y);
		add_edge(2 * n + 3, n + i + 1, k, -x + y);
		add_edge(2 * n + 4, n + i + 1, k,  x + y);
	}
	printf("%lld\n", -min_cost_max_flow(0, 2 * n + 5));
	return 0;
}

```