Description

Ugandan Knuckles is trapped in a dungeon. He wants to find his queen. He finds a stele (碑) that there are n strings on it. You can move the strings in any order you want.

The way to go out is that for each string, all strings placed before it are its substrings.

For example:

If the stele contains strings:

"n"

"ugandan"

"ganda"

"gan"

You should arrange the strings into the order:

"n"

"gan"

"ganda"

"ugandan"

Help Knuckles get out of the dungeon or he will spit on you.

Input

Input contains several lines.

First line contains only one integer n (1<= n <= 1000)

Following n lines, each line contains one string s ( 1<= length of s <= 1000 )

The string s only contains lowercase English letters.

Output

If it's impossible to arrange the strings in the desired order, print "NO".

If it's possible, print "YES" .

And then print n lines each line contains one string in required order.

Remember to print \n at the end of output.

Sample Input  Download

Sample Output  Download

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Description

Recently, scientists finally find a way to produce unlimited energy. The scientists call it "Cat-Toast".

In case that someone might not know:
While buttered toast falls onto the ground, it will always land with its buttered side - Falling Toast Theorem(FTT)
While cats fall onto the ground, they will always land with their four feets. - Falling Cat Theorem(FCT)
By FTT, we can assume that if we put butter on both sides of the toast, we might create a perpetual motion machine, because by FTT, we know that the buttered side will land onto the ground. However, there are two buttered sides. If any side of the toast lands, there will be a contradiction, so the toast will never fall and continue spinning around. We can apply the same way on FCT.
However, there is a big problem. if we just put two buttered toasts or two cats together, there will be no momentum, and obviously it won't spin except for any external force, which cannot be a perpetual motion machine. This problem had confused scientists for centuries.
Recently, scientists finally got a breakthrough progress. They combined a cat and a buttered toast and it just spins by itself! Due to the difference mass of a cat and a buttered toast, the machine itself will provide the momentum to spin, and it will never fall onto the ground (due to the contradiction we proved before), the first perpetual motion machine was born!

The original video is here.

Scientists found that if two cat-toasts' distance are equal to or closer than r, there will be a collision which cause a small black hole and soon disappear, which is very dangerous. The cat-toast must be secured separately. Also, if there are multiple cat-toasts that will collide, those cat-toasts will all collide together and spawn exactly one black hole. If there's any problem, you may refer to Sample I/O.
One day in NTHU, a servitor just carries a lot of cat-toasts, each with a secured box. He accidently falls down and all the cat-toasts just drop out of their own boxes.
Now given r and all the coordinates of all cat-toasts, the servitor wants to know how many cat-toasts remains there after some destructive collisions and how many black holes spawned. 

Note that the distance of two cat-toasts is sqrt( (x1-x2)^2 + (y1-y2)^2 ), where (x1,y1) and (x2,y2) are the coordinates of this two.

Input

The first line contains two integers n, r, indicate the number of cat-toast, the distance r decribed above.
The next n lines, each line contains two integers x_i, y_i, indicates the location of the i-th cat-toast.
1 <= n <= 1000, 1 <= r <= 10⁴
1 <= x_i, y_i <= 10⁴

Output

The first line of the output is the total number of cat-toasts that still remains and the total number of black holes after collisions, separated by a space.
Remember to output a '\n' at the end of the output.
(In fact, except for the problem DO ask you not to output a '\n' at the end of the output, mostly you shoul output a '\n' at the end.)

Take Sample I/O as an example, obviously cat-toast located at (5,15) and (1,15) will collide. (1,7), (1,3), and (5,3) will collide together because (1,7), (1,3) collides, and (1,3), (5,3) collides, just like a chain, or a tree.

There's only one remaining cat-toast located at (500,500) and spawned 2 black holes, so the answer is "1 2" without quotes.

Sample Input  Download

Sample Output  Download

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