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 PYTHON3):

Solution:
# coding: utf-8
# Your code here!
import sys
read = sys.stdin.read
readline = sys.stdin.readline

n, = map(int, readline().split())
xyp = tuple(tuple(map(int, readline().split())) for _ in range(n))

N = 1<<n
INF = 1<<60
resx = []
resy = []
for i in range(n):
    x,y,p = xyp[i]
    rx = [min(abs(x),abs(y))]*N
    ry = [min(abs(x),abs(y))]*N
    for j in range(n):
        for k in range(1<<j):
            rx[k+(1<<j)] = min(rx[k],abs(x-xyp[j][0]))
            ry[k+(1<<j)] = min(ry[k],abs(y-xyp[j][1]))
    
    for j in range(N):
        rx[j] *= p
        ry[j] *= p
    resx.append(rx)
    resy.append(ry)

ans = [INF]*(n+1)
N = 3**n

p = tuple(3**i for i in range(n+1))
rv = [0]*N
rx = [0]*N
ry = [0]*N
for j in range(n):
    for k in range(p[j]):
        rv[k+  p[j]] = rv[k+2*p[j]] = rv[k]
        rv[k] += 1

        rx[k+  p[j]] = rx[k]|(1<<j)
        ry[k+  p[j]] = ry[k]

        rx[k+2*p[j]] = rx[k]
        ry[k+2*p[j]] = ry[k]|(1<<j)

for mask in range(N):
    v = rv[mask]
    x = rx[mask]
    y = ry[mask]
    
    r = 0    
    for i in range(n):
        r += min(resx[i][x],resy[i][y])
    if r < ans[v]:
        ans[v] = r

for i in ans[::-1]:
    print(i)