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:

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

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见题面