Plane Tiling
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:
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 $dy_2$ ($-10^6 \le dx_2, dy_2 \le 10^6$).
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.
Input
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
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.
Samples
4
2 0
0 2
YES
0 0
0 1
1 0
1 1
5
2 6
1 5
NO
2
3 4
1 2
YES
0 0
0 1