Piecewise Linear Function

Points $N$ are given on a two-dimensional coordinate plane. The position of the $i$-th point is $(x_i, y_i)$, and $x_i < x_{i+1}$ holds for every $i$ with $1 \leq i < N$. A linear function connecting point $i$ and point $i+1$ is drawn. Let $F(x)$ be the combination of the $N-1$ linear functions defined on the intervals $(x_1, x_2), (x_2, x_3), \cdots, (x_{N-1}, x_N)$.

For example, when the points are $(0, 0)$, $(1,5)$, $(2,4)$, $(3,3)$, and $(6,10)$, the drawn function is shown below.

For each query, a real number $k$ is given. Determine whether $F(x)$ is increasing or decreasing at $x=k$.

The first line contains the number of points $N$. $(2\leq N \leq 100\,000)$

From the second line onward, the $N$ lines each contain the coordinates $x_i, y_i$ separated by a space. $(-10^9 \leq x_i, y_i \leq 10^9;\ x_i < x_{i + 1})$

The $(N+1)$-th line contains the number of queries $Q$. $(1 \leq Q \leq 100\,000)$

From the $(N+2)$-th line onward, the $Q$ lines each contain a query $k$. $(x_1 < k < x_N;\ k \neq x_i)$

$x_i$ and $y_i$ are integers. Each $k$ is given with at most one digit after the decimal point.

For each query, print $1$ if the linear function containing $k$ is increasing, $-1$ if it is decreasing, and $0$ if it is neither. Print one answer per line, in query order.