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P1019 Mission 1 - III : Run for Explodes

Difficulty: \(\color{brown}420\)

Problem Background

Radar is finally in the Capital of the country, the City of UKE. When he goes in, he suddenly finds that the city has no one in it at all! And he knows that’s not good.

His phone rings…

• Hello, this is AOCode Army Centre. Our brave Radar, be careful now, we have detected that \(n\) explodes is flying to you there. BE CAREFUL!!!!!

Radar looks into the sky. There are hundreds of explodes flying to him from high high in the sky…

Problem Statement

There are \(n\) explodes flying to Radar. and because Radar is RADAR, he knows all locations of the explodes.

When one explode explodes, It will destroy everything in a square of \(\left\lfloor\dfrac{\rm perimetre}{8}\right\rfloor=k\) while it is the centre, and we know it could possibly Destroy Radar!

But Radar is not that easy to die. He has a explode destroyer, which can destroy explodes that centre is in the square of \(\left\lfloor\dfrac{\rm perimetre}{8}\right\rfloor=r\) while it’s centre is Radar.

So please figure out whether Radar could survive in the booming city.

Note that here we think the city of an square of Infinity area with an \(x-\rm axis\) and an \(y-\rm axis\).

Input

The \(1^{st}\) line contains \(3\) integers \(n\), \(r\), \(k\) in this order.

The \(2^{nd}\) line contain \(2\) integers, \(x_0\) and \(y_0\), which is the location of Radar.

Next \((n+1)\) lines, each line contains \(2\) integers \(x_i\) and \(y_i\) (\(1 \le i \le n\)), which is the location of the \(i^{\rm th}\) explode.

Output

Output \(1\) line which contains Yes if Radar could survive, otherwise contains No.

Samples

Input 1

5 8 3
5 5
5 4
4 5
5 6
6 5
8 7

Output 1

Yes

Input 2

5 3 8
5 5
5 4
4 5
5 6
6 5
9 7

Output 2

No

Constraints

• \(1 \le n \le 10^{5}\)
• \(1 \le r \le 200\)
• \(1 \le k \le 300\)
• \(1 \le x_i, y_i \le 1000\ (0 \le i \le n)\)