Parliament

Time Limit: 1 Second    Memory Limit: 32768 KB

New convocation of The Fool Land's Parliament consists of N delegates. According to the present regulation delegates should be divided into disjoint groups of different sizes and every day each group has to send one delegate to the conciliatory committee. The composition of the conciliatory committee should be different each day. The Parliament works only while this can be accomplished.

You are to write a program that will determine how many delegates should contain each group in order for Parliament to work as long as possible.

This problem contains multiple test cases!

The first line of a multiple input is an integer N, then a blank line followed by N input blocks. Each input block is in the format indicated in the problem description. There is a blank line between input blocks.

Input

The input contains a single integer N (5 <= N <= 1000).

Output

Write to the output the sizes of groups that allow the Parliament to work for the maximal possible time. These sizes should be printed on a single line in ascending order and should be separated by spaces.

The output format consists of N output blocks. There is a blank line between output blocks.

Sample Input

2

7

31

Sample Output

3 4
 
2 3 5 6 7 8

Submit

Source: Northeastern Europe 1998