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? \includegraphics{https://static.eolymp.com/content/6d/6db0584145bbb05bdec7ef5840d57e6cf12f0142.gif} 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 $P_iP_{i+1}$). \InputFile 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 $P_i\:(0 \le x_1 < x_2 <... < x_n \le 10^9, 0 \le y_i \le 10^9)$. \OutputFile 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.