A. Integer Sequence Dividing
math
You are given an integer sequence \(1, 2, \dots, n\). You have to divide it into two sets \(A\) and \(B\) in such a way that each element belongs to exactly one set and \(|sum(A) - sum(B)|\) is minimum possible.The value \(|x|\) is the absolute value of \(x\) and \(sum(S)\) is the sum of elements of the set \(S\).
The first line of the input contains one integer \(n\) (\(1 \le n \le 2 \cdot 10^9\)).
Print one integer — the minimum possible value of \(|sum(A) - sum(B)|\) if you divide the initial sequence \(1, 2, \dots, n\) into two sets \(A\) and \(B\).
Some (not all) possible answers to examples:In the first example you can divide the initial sequence into sets \(A = \{1, 2\}\) and \(B = \{3\}\) so the answer is \(0\).In the second example you can divide the initial sequence into sets \(A = \{1, 3, 4\}\) and \(B = \{2, 5\}\) so the answer is \(1\).In the third example you can divide the initial sequence into sets \(A = \{1, 4, 5\}\) and \(B = \{2, 3, 6\}\) so the answer is \(1\).