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>

using ll = long long;
const int maxn = 16;

int n;
struct pt {
    ll x, y, p;
    void read() {
        scanf("%lld%lld%lld", &x, &y, &p);
    }
} p[maxn];

ll d[1 << maxn][maxn][2], ans[maxn];

int main() {
    scanf("%d", &n);
    for(int i = 0; i < n; ++i) {
        p[i].read();
    }
    for(int i = 0; i <= n; ++i) {
        ans[i] = 1e18;
    }
    for(int s = 0; s < (1 << n); ++s) {
        for(int i = 0; i < n; ++i) {
            d[s][i][0] = std::abs(p[i].x);
            d[s][i][1] = std::abs(p[i].y);
            for(int j = 0; j < n; ++j) {
                if(~s & (1 << j))
                    continue;
                d[s][i][0] = std::min(d[s][i][0], std::abs(p[i].x - p[j].x));
                d[s][i][1] = std::min(d[s][i][1], std::abs(p[i].y - p[j].y));
            }
        }
    }
    for(int s = 0; s < (1 << n); ++s) {
        int w = __builtin_popcount(s);
        for(int u = s; u >= 0; u = (u - 1) & s) {
            int v = s ^ u;
            ll tot = 0;
            for(int i = 0; i < n; ++i) {
                tot += p[i].p * std::min(d[u][i][0], d[v][i][1]);
            }
            ans[w] = std::min(ans[w], tot);
            if(u == 0)
                break;
        }
    }
    for(int i = 0; i <= n; ++i) {
        printf("%lld\n", ans[i]);
    }
    return 0;
}