Integer Sequence Dividing
Description
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 $B$.
Input
The first line of the input contains one integer $n$ ($1 \le n \le 2 \cdot 10^9$).
Output
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 $B$.
Samples
3
0
5
1
6
1
Note
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 $1$.