That's a long one....isn't it?

Algebra Level 4

Let \(P(x) = x^6 + ax^5 + bx^4 + cx^3 + dx^2 + ex +f\) be a polynomial such that

\(P(1) =1\) , \(P(2) = 2\) , \(P(3) = 3\) , \(P(4) = 4\) , \(P(5) = 5\) and \(P(6) = 6\).