Circle Selection

There are $n$ circles $c_1, c_2, \dots, c_n$ on the plane. Repeat the following steps.

1. Take the circle $c_i$ with the largest radius. If several circles share the largest radius, take the one with the smallest index.
2. Remove $c_i$ and every circle that intersects $c_i$. Two circles intersect if at least one point is contained in both of them. A point is contained in a circle if it lies inside the circle or on its border.
3. Repeat steps 1 and 2 until no circle is left.

If the circle taken in the round that removes $c_i$ is $c_j$, then $c_j$ eliminates $c_i$. The circle taken in a round is removed in that same round, so a circle can eliminate itself. For every circle, find the index of the circle that eliminates it.

The first line contains the number of circles $n$ ($1 \le n \le 3 \times 10^5$).

Each of the next $n$ lines contains three integers $x_i$, $y_i$, $r_i$, the x-coordinate, the y-coordinate and the radius of circle $c_i$ ($-10^9 \le x_i, y_i \le 10^9$, $1 \le r_i \le 10^9$).

Print the integers $a_1, a_2, \dots, a_n$ on the first line, separated by single spaces. $a_i$ is the index of the circle that eliminates $c_i$.

The picture in the statement shows the first example.