TWINSNOW - Snowflakes

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You may have heard that no two snowflakes are alike. Your task is to write a program to determine whether this is really true. Your program will read information about a collection of snowflakes, and search for a pair that may be identical. Each snowflake has six arms. For each snowflake, your program will be provided with a measurement of the length of each of the six arms. Any pair of snowflakes which have the same lengths of corresponding arms should be agged by your program as possibly identical.

Input

- The first line of input will contain a single integer n; the number of snowflakes to follow.
- This will be followed by n lines, each describing a snowflake. Each snowflake will be described by a line containing six integers (each integer is at least 0 and less than 10000000), the lengths of the arms of the snowflake. The lengths of the arms will be given in order around the snowflake (either clockwise or counterclockwise), but they may begin with any of the six arms. For example, the same snowflake could be described as 1 2 3 4 5 6 or 4 3 2 1 6 5.

Output

If all of the snowflakes are distinct, your program should print the message:

No two snowflakes are alike.

If there is a pair of possibly identical snowflakes, your program should print the message:

Twin snowflakes found.

Sample

Input:
2
1 2 3 4 5 6
3 4 5 6 1 2

Output:
Twin snowflakes found.

Limitations

- 0 < n ≤ 105.


hide comments
BornIdiot: 2009-10-09 05:26:16

2
2 3 1 4 5 6
1 2 3 4 5 6
For this test case,i think ans should be no
but ans getting uploaded gives yes

Brian Bi: 2009-05-30 13:47:20

I assume what they actually mean is that two snowflakes are considered alike if one can be possibly rotated and possibly flipped such that it coincides with the other. However, read my other comment below...

Max: 2009-05-26 12:49:08

Any pair of snowflakes which have the same lengths of CORRESPONDING arms should be agged by your program as possibly identical.

I think this is not true

Last edit: 2009-05-26 12:49:20
amaroq: 2009-05-12 21:00:40

I responded to a comment made by Critical Thinking, but that doesn't make much sense now because he deleted it.
I agree with you: the test data is too weak and should be improved.

Brian Bi: 2009-05-12 14:23:03

I don't understand what these comments mean...

Brian Bi: 2009-05-11 23:09:43

The test data is very weak: it suffices to sort the lengths of the arms of each snowflake. (Yes, I know it was actual test data from the CCC, we have it up on our judge too.) Can you add some cases that will make this approach fail?

Last edit: 2009-05-11 23:10:07

Added by:AnhDQ
Date:2009-05-11
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:CCC07