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Problem E
Divisor Counts

Given a positive integer $N$, compute the number of divisors for all integers $1 \le i \le N$.

Input

The first line contains the integer $N$ ($1 \le N \le 3\, 000\, 000$).

Output

For each $i$ between $1$ and $N$, output a line with the number of positive divisors of $i$.

Sample Input 1 Sample Output 1
12
1
2
2
3
2
4
2
4
3
4
2
6

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