13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T65e,

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

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

Plane Tiling

Examples