Run Direction

Suzumo is the coach of the ChefLand OI team. Physical condition is very important in any olympiad, so he wants to make the children run a bit as a warmup. The team consists of $N$ children numbered $1$ through $N$ standing at some positions on the $x$-axis. For each valid $i$, the initial $x$-coordinate of the $i$-th kid is $x_i$, the running velocity of the $i$-th kid is constant and equal to $v