I. Plane Tilingtime limit per test1 secondmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou 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}  InputThe 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).OutputIf 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.ExamplesInput
4
2 0
0 2
Output
YES
0 0
0 1
1 0
1 1
Input
5
2 6
1 5
Output
NO
Input
2
3 4
1 2
Output
YES
0 0
0 1

4
2 0
0 2

YES 0 0 0 1 1 0 1 1 
['geometry', 'implementation', 'math', '*2500']