Third Permutation

You are given two permutations a and b such that a_i \neq b_i in every position. Create a third permutation c such that a_i \neq c_i and b_i \neq c_i in every position.

Input

The first line has an integer n: the permutation size. The second line has n integers a_1,a_2,\dots,a_n. The third line has n integers b_1,b_2,\dots,b_n.

Output

Print n integers c_1,c_2,\dots,c_n. You can print any valid solution. If there are no solutions, print IMPOSSIBLE.

Constraints

$2 \le n \le 10^5$

Example

Input

5
1 3 2 5 4
4 1 3 2 5

Output

3 2 5 4 1