Mountainous landscape
Mountainous landscape
You travel through a scenic landscape consisting mostly of mountains — there are n landmarks (peaks and valleys) on your path. You pause for breath and wonder: which mountain are you currently seeing on the horizon?
Formally: you are given a polygonal chain P_1P_2...P_n in the plane. The x coordinates of the points are in strictly increasing order. For each segment P_iP_{i+1} of this chain, find the smallest index j > i, for which any point of P_jP_{j+1} is visible from P_iP_{i+1} (lies strictly above the ray P_iP_{i+1}).
Input data
The first line contains the number of test cases T. The descriptions of the test cases follow:
The first line of each test case contains an integer n\:(2 \le n \le 10^5) — the number of vertices on the chain. Each of the following n lines contains integer coordinates x_i, y_i of the vertex P_i\:(0 \le x_1 < x_2 <... < x_n \le 10^9, 0 \le y_i \le 10^9).
Output data
For each test case, output a single line containing n - 1 space-separated integers. These should be the smallest indices of chain segments visible to the right, or 0 when no such segment exists.
Examples
2 8 0 0 3 7 6 2 9 4 11 2 13 3 17 13 20 7 7 0 2 1 2 3 1 4 0 5 2 6 1 7 3
0 3 6 5 6 0 0 6 4 4 0 6 0