Third Permutation · CODER HUSC

Time limit: 1.0 s
Memory limit: 256 MB
Points: 10partial
AC rate: 60.0%
Solvers: 2

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

Input

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

Output

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

Constraints

$2 \le n \le 10^5$ ~2 \le n \le 10^5~

Example

Input:

Output:

3 2 5 4 1

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