Description:
You are given five integers $$$n$$$, $$$dx_1$$$, $$$dy_1$$$, $$$dx_2$$$ and $$$dy_2$$$. You have to select $$$n$$$ distinct pairs of integers $$$(x_i, y_i)$$$ in such a way that, for every possible pair of integers $$$(x, y)$$$, there exists exactly one triple of integers $$$(a, b, i)$$$ meeting the following constraints:
$$$ \begin{cases} x \, = \, x_i + a \cdot dx_1 + b \cdot dx_2, \\ y \, = \, y_i + a \cdot dy_1 + b \cdot dy_2. \end{cases} $$$
Input Format:
The first line contains a single integer $$$n$$$ ($$$1 \le n \le 10^5$$$).
The second line contains two integers $$$dx_1$$$ and $$$dy_1$$$ ($$$-10^6 \le dx_1, dy_1 \le 10^6$$$).
The third line contains two integers $$$dx_2$$$ and $$$dy_2$$$ ($$$-10^6 \le dx_2, dy_2 \le 10^6$$$).
Output Format:
If it is impossible to correctly select $$$n$$$ pairs of integers, print NO.
Otherwise, print YES in the first line, and then $$$n$$$ lines, the $$$i$$$-th of which contains two integers $$$x_i$$$ and $$$y_i$$$ ($$$-10^9 \le x_i, y_i \le 10^9$$$).
If there are multiple solutions, print any of them.
Note:
None