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