Position Zero

Banana is a stage girl. She wants to stand at the "Position Zero" of the stage. In this problem, the stage is a two-dimensional coordinate plane, and "Position Zero" is expressed as a circle on this plane.

The center of "Position Zero" is $(X, Y)$, and its radius is $R$.

However, the range where Banana can move is limited. Banana chooses one of $N$ straight lines and can move only along it.

Each line is expressed as $x = T_{i}$ $(1 \leq i \leq N)$.

Given $N$, the number of lines Banana can move along, the center coordinates $X$, $Y$ and radius $R$ of "Position Zero", and the information $T_i$ of each line, output $A$, the number of lines along which Banana can enter the inside of "Position Zero", and $B$, the number of lines along which Banana can enter only the boundary of "Position Zero".

The first line contains the number of lines $N$ along which Banana can move.

The second line contains three integers $X$, $Y$, and $R$, separated by spaces.

From the third line to the $(N + 2)$-th line, the value $T_i$ is given in order on the $(i + 2)$-th line $(1 \leq i \leq N)$.

All numbers given in the input are integers.

Print $A$ and $B$, separated by a space, where $A$ is the number of lines along which Banana can enter the inside of "Position Zero", and $B$ is the number of lines along which Banana can enter only the boundary of "Position Zero".

• $1 \leq N \leq 100$
• $-100 \leq X, Y \leq 100$
• $1 \leq R \leq 100$
• $-100 \leq T_{i} \leq 100$ $(1 \leq i \leq N)$