Problem G. Interstellar Travel

After trying hard for many years, Little Q has finally received an astronaut license. To celebrate the fact, he intends to buy himself a spaceship and make an interstellar travel.
Little Q knows the position of $n$ planets in space, labeled by $1$ to $n$. To his surprise, these planets are all coplanar. So to simplify, Little Q put these $n$ planets on a plane coordinate system, and calculated the coordinate of each planet $(x_i,y_i)$.
Little Q plans to start his journey at the $1$-th planet, and end at the $n$-th planet. When he is at the $i$-th planet, he can next fly to the $j$-th planet only if $x_i<x_j$, which will cost his spaceship $x_i\times y_j-x_j\times y_i$ units of energy. Note that this cost can be negative, it means the flight will supply his spaceship.
Please write a program to help Little Q find the best route with minimum total cost.

The first line of the input contains an integer $T(1\leq T\leq10)$, denoting the number of test cases.
In each test case, there is an integer $n(2\leq n\leq 200000)$ in the first line, denoting the number of planets.
For the next $n$ lines, each line contains $2$ integers $x_i,y_i(0\leq x_i,y_i\leq 10^9)$, denoting the coordinate of the $i$-th planet. Note that different planets may have the same coordinate because they are too close to each other. It is guaranteed that $y_1=y_n=0,0=x_1<x_2,x_3,...,x_{n-1}<x_n$.

For each test case, print a single line containing several distinct integers $p_1,p_2,...,p_m(1\leq p_i\leq n)$, denoting the route you chosen is $p_1\rightarrow p_2\rightarrow...\rightarrow p_{m-1}\rightarrow p_m$. Obviously $p_1$ should be $1$ and $p_m$ should be $n$. You should choose the route with minimum total cost. If there are multiple best routes, please choose the one with the smallest lexicographically.
A sequence of integers $a$ is lexicographically smaller than a sequence of $b$ if there exists such index $j$ that $a_i = b_i$ for all $i < j$, but $a_j < b_j$.

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2018 Multi-University Training Contest 3