Problem: New AtCoder City has an infinite grid of streets, as follows:

* At the center of the city stands a clock tower. Let (0, 0) be the coordinates of this point.
* A straight street, which we will call East-West Main Street, runs east-west and passes the clock tower. It corresponds to the x-axis in the two-dimensional coordinate plane.
* There are also other infinitely many streets parallel to East-West Main Street, with a distance of 1 between them. They correspond to the lines \ldots, y = -2, y = -1, y = 1, y = 2, \ldots in the two-dimensional coordinate plane.
* A straight street, which we will call North-South Main Street, runs north-south and passes the clock tower. It corresponds to the y-axis in the two-dimensional coordinate plane.
* There are also other infinitely many streets parallel to North-South Main Street, with a distance of 1 between them. They correspond to the lines \ldots, x = -2, x = -1, x = 1, x = 2, \ldots in the two-dimensional coordinate plane.



There are N residential areas in New AtCoder City. The i-th area is located at the intersection with the coordinates (X_i, Y_i) and has a population of P_i. Each citizen in the city lives in one of these areas.

The city currently has only two railroads, stretching infinitely, one along East-West Main Street and the other along North-South Main Street.
M-kun, the mayor, thinks that they are not enough for the commuters, so he decides to choose K streets and build a railroad stretching infinitely along each of those streets.

Let the walking distance of each citizen be the distance from his/her residential area to the nearest railroad.
M-kun wants to build railroads so that the sum of the walking distances of all citizens, S, is minimized.

For each K = 0, 1, 2, \dots, N, what is the minimum possible value of S after building railroads?

Constraints

* 1 \leq N \leq 15
* -10 \ 000 \leq X_i \leq 10 \ 000
* -10 \ 000 \leq Y_i \leq 10 \ 000
* 1 \leq P_i \leq 1 \ 000 \ 000
* The locations of the N residential areas, (X_i, Y_i), are all distinct.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
X_1 Y_1 P_1
X_2 Y_2 P_2
:  :  :
X_N Y_N P_N


Output

Print the answer in N+1 lines.
The i-th line (i = 1, \ldots, N+1) should contain the minimum possible value of S after building railroads for the case K = i-1.

Examples

Input

3
1 2 300
3 3 600
1 4 800


Output

2900
900
0
0


Input

5
3 5 400
5 3 700
5 5 1000
5 7 700
7 5 400


Output

13800
1600
0
0
0
0


Input

6
2 5 1000
5 2 1100
5 5 1700
-2 -5 900
-5 -2 600
-5 -5 2200


Output

26700
13900
3200
1200
0
0
0


Input

8
2 2 286017
3 1 262355
2 -2 213815
1 -3 224435
-2 -2 136860
-3 -1 239338
-2 2 217647
-1 3 141903


Output

2576709
1569381
868031
605676
366338
141903
0
0
0

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#define SIZE 20
#define BT (1<<16)
#define INF 1000000000000000LL
using namespace std;
typedef long long int ll;

int X[SIZE],Y[SIZE],P[SIZE];
ll score[BT];
ll dp[BT][SIZE];

int main()
{
	int n;
	scanf("%d",&n);
	for(int i=0;i<n;i++) scanf("%d %d %d",&X[i],&Y[i],&P[i]);
	for(int S=1;S<1<<n;S++)
	{
		score[S]=INF;
		for(int i=0;i<n;i++)
		{
			int x=X[i];
			ll sx=0;
			for(int k=0;k<n;k++) if(S>>k&1) sx+=(ll) abs(X[k]-x)*(ll) P[k];
			score[S]=min(score[S],sx);
			
			int y=Y[i];
			ll sy=0;
			for(int k=0;k<n;k++) if(S>>k&1) sy+=(ll) abs(Y[k]-y)*(ll) P[k];
			score[S]=min(score[S],sy);
		}
	}
	for(int S=0;S<1<<n;S++)
	{
		ll score=0;
		for(int k=0;k<n;k++) if(S>>k&1) score+=(ll) min(abs(X[k]),abs(Y[k]))*(ll) P[k];
		for(int k=0;k<=n;k++)
		{
			dp[S][k]=score;
		}
	}
	for(int k=0;k<=n;k++) dp[0][k]=0;
	for(int S=0;S<1<<n;S++)
	{
		for(int k=0;k<n;k++)
		{
			if(dp[S][k]==INF) continue;
			int Z=(1<<n)-1-S;
			for(int T=Z;T>0;T=(T-1)&Z)
			{
				dp[S|T][k+1]=min(dp[S|T][k+1],dp[S][k]+score[T]);
			}
		}
	}
	for(int i=0;i<=n;i++) printf("%lld\n",dp[(1<<n)-1][i]);
}