Professor Doge is now working on a project using polynomial for some mathematical calculations. In his project, he wants to approximate the exponential function e
x with a polynomial whose degree does not exceed n. As one of professor’s assistants, you are asked to find a polynomial f (x) with degree n that minimizes
There are several test cases, please process till EOF.
Each test case consists of only one integer denoting the degree n of the polynomial (0 ≤ n ≤ 10).
For each test case, print n + 1 lines.
for the i-th line, print one floating number a
i denoting the coefficient in the term x
i, i = 0, 1, . . . , n.
It is guaranteed that the answer is always unique. Any answer within an absolute error less than or equal to 10
-50 would be accepted.