A permutation of integers $1,2,\ldots,n$ is called beautiful if there are no adjacent elements whose difference is $1$ .
Given $n$ , construct a beautiful permutation if such a permutation exists.
The only input line contains an integer $n$ .
Print a beautiful permutation of integers $1,2,\ldots,n$ . If there are several solutions, you may print any of them. If there are no solutions, print "NO SOLUTION".