Maths

시간 제한1초메모리 제한1024 MB

요약

k가 2부터 n까지일 때 각 접두사 합이 정확히 a_k개의 양의 약수를 갖는 수열을 찾는다.

난이도: 보통10점 중 4점
유형: 수학, 정수론, 그리디, 구현
정답자: 아직 제출이 없습니다

문제

Android Vasya attends Maths classes. His group started to study the number theory recently. The teacher gave them several tasks as a homework. One of them is as follows.

There is an integer $n$ . The problem is to find a sequence of integers $a\_1, \ldots, a\_n$ such that for any $k$ from 2 to $n$ the sum $a\_1 + \ldots + a\_k$ has exactly $a\_k$ different positive divisors. Help Vasya to cope with this task.

입력

The only line contains an integer $n$ ( $2 \leq n \leq 100\\,000$ ).

출력

If there is no such sequence output Impossible. Otherwise output space-separated integers $a\_1, \ldots, a\_n$ ( $1 \leq a\_i \leq 300$ ).

예제1

예제 1
입력
```
3
```
예상 출력
```
1 3 4
```