Birthday Cake

John's parents made him a huge birthday cake for his birthday. Dinner is over, so it is time to eat the cake. There are $n$ candles on the cake. John wants to cut the cake into $n$ pieces so that every piece carries exactly one candle and no piece is left over. He made $m$ straight cuts across the cake. Check whether his cuts divide the candles the way he wants.

The cake is a circle of radius $r$ centered at $(0, 0)$. The candles are $n$ distinct points strictly inside the circle. Each cut is a straight line $ax + by + c = 0$ given by three coefficients $a$, $b$, and $c$.

The first line has three integers $n$ ($1 \le n \le 50$), $m$ ($1 \le m \le 15$), and $r$ ($1 \le r \le 100$).

Each of the next $n$ lines gives the location of one candle as two integers $x$ and $y$ ($0 \le \sqrt{x^2 + y^2} < r$).

Each of the next $m$ lines gives the coefficients of one cut as three integers $a$, $b$, and $c$ ($0 \le |a|, |b| \le 100$, $0 \le |c| \le 20000$) describing the line $ax + by + c = 0$. The values $a$ and $b$ are never both $0$.

All candles are distinct and all lines are distinct. No candle lies on a cut. No line misses the cake completely or only touches it at one point. The number of cake pieces stays the same if any one cut is moved by at most $10^{-4}$ in any direction. Every candle also stays in the interior of the same piece if it is moved by at most $10^{-4}$ in any direction.

Print yes if the cuts divide the cake so that every piece carries exactly one candle. Otherwise print no.