# Chasing Chmyaaax

You have learned that the evil Chmyaaax has escaped to the Link-Cut system, and you have set out to pursue him. Unfortunately, after his defeat, he managed to do one little dirty trick: he broke your fuel tank, and now it's empty. Now you have only one means of transportation left: Gravitational maneuvers!

The space where the events take place can be represented as a $XY$-plane. Initially, you are at position $(s_{x},s_{y})$. There are $n$ meteors in the space, each determined by its location $(mx_{i},my_{i})$. Since your ship was built by Lucy, gravitational maneuvers work non-standardly. Specifically, you can choose two meteors and mirror your position relative to the middle of the path between them. There is an infinite vertical line at $x$ = $r$ coordinate that separates our Solar system from the Link-Cut system. To enter the Link-Cut system your $x$-coordinate needs to be at least $r$.

Formally, let $(x_{i},y_{i})$ be the position of the $i$-th meteor and let $(s_{x},s_{y})$ be your initial position. Then each maneuver can be described by a pair of indices $i$ and $j$:

If your current position is $(px,py)$, then it will become $(2mx_{i}+mx_{j} −(px−2mx_{i}+mx_{j} ),2my_{i}+my_{j} −(py−2my_{i}+my_{j} ))$.

Here is the example of how maneuver works:

Maneuver from point $P_{old}$ to point $P_{new}$ relative to the middle of the way between meteors $m_{1}$ and $m_{2}$

Now Lucy is preparing the ship for maneuvers and she needs to know the minimum number of maneuvers required for you to enter the Link-Cut system. Help her with this challenging task or determine it is impossible.

## Input

The first line contains two integers $n$ and $r$ $(2≤n≤2⋅10_{5},0≤r≤10_{15})$ — the number of meteors and the $x$-coordinate, from which the Link-Cut system starts off.

The second line contains two integers $s_{x}$ and $s_{y}$ $(0≤s_{x},s_{y}≤10_{15})$ — your initial position.

Each of the next $n$ lines contains a pair of integers $mx_{i}$ and $my_{i}$ $(0≤mx_{i},my_{i}≤10_{15})$ — the location of the $i$-th meteor.

Please note that some positions (including yours) can be the same.

## Output

In the only line, you need to output the minimum number of maneuvers required for you to enter the Link-Cut system. If it is impossible to reach it, output "`Chmyaaaax has escaped`

".

## Examples

## Note

The first example is shown in the picture in the statement: $P_{old}(0;0)$ is your initial point and $P_{new}(7;4)$ is your new point after performing one maneuver relative to the middle of the way between the only two meteors. $7≥r=6$, which means that you will enter the Link-Cut system after this operation. And initially your $x$-coordinate is $0$, which is less than $r=6$, thus the answer cannot be $0$.

## Scoring

($31$ points): $mx_{1},my_{1},mx_{2},my_{2}≥r$;

($71$ points): $r,mx_{i},my_{i}≤10_{5}$;

($99$ points): $r,mx_{i},my_{i}≤10_{8}$;

($49$ points): no additional constraints.