A11692 | Ghosts

The first line contains three integers $n$ , $a$ and $b$ ( $1 \leq n \leq 200000$ , $1 \leq |a| \leq 10^9$ , $0 \le |b| \le 10^9$ ) — the number of ghosts in the universe and the parameters of the straight line.

Each of the next $n$ lines contains three integers $x_i$ , $V_{xi}$ , $V_{yi}$ ( $-10^9 \leq x_i \leq 10^9$ , $-10^9 \leq V_{x i}, V_{y i} \leq 10^9$ ), where $x_i$ is the current $x$ -coordinate of the $i$ -th ghost (and $y_i = a \cdot x_i + b$ ).

It is guaranteed that no two ghosts share the same initial position, in other words, it is guaranteed that for all $(i,j)$ $x_i \neq x_j$ for $i \ne j$ .

Output one line: experience index of the ghost kind $GX$ in the indefinite future.

There are four collisions $(1,2,T-0.5)$ , $(1,3,T-1)$ , $(2,4,T+1)$ , $(3,4,T+0.5)$ , where $(u,v,t)$ means a collision happened between ghosts $u$ and $v$ at moment $t$ . At each collision, each ghost gained one experience point, this means that $GX = 4 \cdot 2 = 8$ .

In the second test, all points will collide when $t = T + 1$ .

The red arrow represents the 1-st ghost velocity, orange represents the 2-nd ghost velocity, and blue represents the 3-rd ghost velocity.