Problem L. Limited permutation ≡

Statement

There are two integer arrays A and B, of length N each.

Your program must generate lexicographically minimal permutation of A, satisfying conditions:

A_i ≤ B_i, i = 1, 2, …, N

Input format

Input contains integer N, followed by 2 ⋅ N integers: array A, then array B.

Output format

Output must contain N integers — resulting permutation.

If the solution does not exist, output a single number  − 1.

Constraints

0 ≤ A_i, B_i ≤ 10⁹, 1 ≤ N ≤ 2 ⋅ 10⁵

Sample tests

5
1 9 3 7 5
9 3 9 1 9

5 3 7 1 9

5
1 9 3 7 5
9 3 3 1 7

-1