Distance to Polygon

Input

The first line contains the integer $n$ ( $3 \leq n \leq 4000$ 3 \leq n \leq 4000) — the number of vertices of the polygon.

The following $n$ lines list the coordinates of the vertices in counterclockwise order. No three vertices are collinear. Each vertex is given by two integers $x$ , $y$ ( $- 15000 \leq x, y \leq 15000$ -15000 \leq x, y \leq 15000).

The next line contains five integers: $q$ , $a$ , $b$ , $c$ , $d$ ( $1 \leq q \leq 1 0^{6}$ 1 \leq q \leq 10^6, $0 \leq a, b, c, d \leq 15000$ 0 \leq a, b, c, d \leq 15000) — the number of queries and the coefficients for calculating the coordinates of subsequent queries using the coordinates and result of the previous query.

The last line contains two integers $x_{1}$ x_1, $y_{1}$ y_1 ( $- 15000 \leq x_{1}, y_{1} \leq 15000$ -15000 \leq x_1, y_1 \leq 15000) — the coordinates of the first query point.

The coordinates of each subsequent query are computed using the coordinates and the result of the previous query as follows. If for the $i$ -th query the coordinates are $x_{i}$ x_i, $y_{i}$ y_i, and the answer is $d_{i}$ d_i, then the coordinates for the $(i + 1)$ (i+1)-th query are:

x_{i + 1} = ((x_{i} + 15000) \cdot (round (d_{i}) + a) + b) mod 30001 - 15000; y_{i + 1} = ((y_{i} + 15000) \cdot (round (d_{i}) + c) + d) mod 30001 - 15000;

x_{i+1} = ((x_i + 15000) \cdot (\operatorname{round}(d_i) + a) + b) \bmod 30001 - 15000; y_{i+1} = ((y_i + 15000) \cdot (\operatorname{round}(d_i) + c) + d) \bmod 30001 - 15000;

Here $round (d_{i})$ \operatorname{round}(d_i) means rounding $d_{i}$ d_i to the nearest integer.

Output

Print a single number — the answer to the last query, with an absolute or relative error not exceeding $1 0^{- 8}$ 10^{-8}.

Examples

Example 1

Loading