You are given a set $P$ with $n$ points in the 2-dimensional plane. We want to know if a point $w$ can be written as a linear combination of points from $R$, where $R \subseteq P$, that is:
$w = \displaystyle\sum_{i=1}^{|R|} {\mu}_i \cdot R_i$
such that ${\mu}_i \ge 0$ for $i = 1,2,...,|R|$ and $\displaystyle\sum_{i=1}^{|R|} {\mu}_i = 1$.
For each point $w$ you should find a set $R$ with at most 5 elements ($|R| \le 5$) such that coefficients satisfy previous rule, or tell if such representation doesn't exist..
Notes:
First line of input contains an integer $n$ $(1 \leq n \leq 10^5)$, the number of points in $P$.
Next $n$ lines contains two integers $x_i, y_i$ $(0 \le x_i, y_i \le 10^9)$, the coordinates of the $i$-th point.
Next line contains an integer $q$ $(1 \le q \le 10^4)$, representing the amount of points $w$ to answer.
The remaining $q$ lines contains two integers $x_w, y_w(0 \le x_w, y_w \le 10^9)$, the coordinates of each point $w$.
For each point $w$:
Then print $m$ lines, each of them with an integer $i$ indicating that the $i$-th point of $P$ belongs to $R$, followed by a real number $\mu_i$ indicating its coefficient.
Note: Your solution will be considered correct if it follows all the described restrictions and the squared distance between $w$ and the point $w' = \displaystyle\sum_{i=1}^{|R|} {\mu}_i \cdot R_i$ obtained does not exceed $10^{-5}$.