Permutation Prime Sums

Given n, create two permutations a and b of size n such that a_i+b_i is prime for i=1,2,\dots,n.

Input

The only line has an integer n.

Output

Print two permutations. You can print any valid solution. If there are no solutions, print IMPOSSIBLE.

Constraints

$1 \le n \le 10^5$

Example

Input

5

Output

2 1 3 5 4
5 1 4 2 3

Explanation: The sums are 2+5=7, 1+1=2, 3+4=7, 5+2=7 and 4+3=7 which all are primes.