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He is well known for arpa's trick .

If u had to say this then why u put that poll thing .

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That is all right but any special reasoning happening such pattern.To observe it is a good thing but to analyse and getting to prove side of it is best.I am not to able to convey what i want .But something to prove this observation might help me in what i want.

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reasonings of such patterns?

c[i][j] = k + 1; is another small mistake i think.it should be k-1.but it doesnt affect the ans