A group of sages had a very lively
discussion of sophisticated topics. After a while, feeling quite tired, they
thought that some good tea and a big tasty apple pie would make them feel much
better. However, the sages found it boring to cut the pie into equal pieces, so
they took a more challenging path. The first sage takes 1/k1-th
part of the whole pie, the second 1/k2-th, the third
1/k3-th and so on. Here, the numbers k1,
k2, k3, … kn
are different positive integers not exceeding 100 (even the wisest sage is
unable to precisely cut off less than 1/100 of a pie).
Your task is to write a program that will
split the pie in such a way that each sage gets 1/ki-th
of the whole pie (the pie must be shared without remainder!), or report that it
is impossible to split the pie under these conditions. In case of several
possible solutions, any of them will be considered correct.
Limitations
1 £
n £ 20;
k1, k2, …, kn
are positive integer numbers, 1 £
ki £ 100;
1/k1 + 1/k2
+ 1/k3 + … + 1/kn = 1;
ki ≠ kj, for any i, j, i ≠ j.
Input
The input file contains a single integer n,
the number of sages sharing the pie.
Output
The output file should contain n
space-delimited integers k1, k2,
…, kn. If there is no solution then the output file
should contain the message “No solution” (without quotation marks).
Example
|
Input
|
Output
|
|
3
|
2 3 6
|
|
2
|
No solution
|
|
1
|
1
|
|
4
|
2 4 6 12
|
