Find the Outlier
Professor Abacus has just built a new computing engine for making numerical tables. It was designed to calculate the values of a polynomial function in one variable at several points at a time. With the polynomial function f(x)=x^2+2x+1, for instance, a possible expected calculation result is 1 (= f(0)), 4 (= f(1)), 9 (= f(2)), 16 (= f(3)), and 25 (= f(4)).
It is a pity, however, the engine seemingly has faulty components and exactly one value among those calculated simultaneously is always wrong. With the same polynomial function as above, it can, for instance, output 1, 4, 12, 16, and 25 instead of 1, 4, 9, 16, and 25.
You are requested to help the professor identify the faulty components. As the rst step, you should write a program that scans calculation results of the engine and nds the wrong values.
Input
The input is a sequence of datasets, each representing a calculation result in the following format.
d
v_0
v_1
...
v_{d+2}
Here, d in the rst line is a positive integer that represents the degree of the polynomial, namely, the highest exponent of the variable. For instance, the degree of 4x^5+3x+0.5 is ve and that of 2.4x+3.8 is one. d is at most five.
The following d+3 lines contain the calculation result of f(0), f(1), ..., and f(d+2) in this order, where f is the polynomial function. Each of the lines contains a decimal fraction between -100.0 and 100.0, exclusive.
You can assume that the wrong value, which is exactly one of f(0), f(1), ..., and f(d+2), has an error greater than 1.0. Since rounding errors are inevitable, the other values may also have errors but they are small and never exceed 10^{-6}.
The end of the input is indicated by a line containing a zero.
Output
For each dataset, output i in a line when v_i is wrong.