Strange order
Given an integer n. Initially you have permutation p of size n: \(p_i = i\). To build new array a from p following steps are done while permutation p is not empty:
- Choose maximum existing element in p and define it as x;
- Choose all such y in p that \(\gcd(x, y) \neq 1\);
- Add all chosen numbers into array a in decreasing order and remove them from permutation.
Your task is to find a after p became empty.
Note: \(\gcd(a, b)\) is the greatest common divisor of integers a and b.
Input format
Input contains single integer n (\(1 \leq n \leq 2 \cdot 10^6\)) — the size of permutation p.
Output format
Print n integers — array a.
Explanation
It's needed 4 iterations to create array a:
- Add 5
- Add 4 and 2
- Add 3
- Add 1
Time Limit:
2.0 sec(s)
for each input file.
Memory Limit:
512 MB
Source Limit:
1024 KB
Marking Scheme:
Marks are awarded when all the testcases pass.
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