Sigma Arrays

You are given two arrays A and B, each containing N number of distinct positive integers. In other words, A and B are sets of positive integers such that \(n(A) = n(B) = N\). But a number in A can appear in B and vice versa.

For each integer (A_i ) in A , you need to pair it with an integer (B_j ) in B. You are not allowed to pick the same integer (B_j ) from B more than once.

If it’s possible to create N pairs such that the sum of each pair is the same, then the two arrays are considered as Sigma Arrays.

Given two arrays, your task is to determine whether they are Sigma Arrays, AND if they are Sigma Arrays, create N pairs of integers that display this quality.

Input Format

First line contains a single integer N, the number of elements in each array.
Next line contains N integers, the elements of the array A, with i ^th of them being A_i.
Last line contains N integers, the elements of the array B, with i ^th of them being B_i.

Output Format

If they are Sigma Arrays, print N lines, each containing a pair (A_i , B_j ), sorted in the increasing order of A_i.
If the two arrays are not Sigma Arrays, print -1

Refer the samples for a clearer picture.

Constraints

• 1 \(\leq\) N \(\leq\) 10⁵
• 1 \(\leq\) A_i , B_i \(\leq\) 10⁹

Limits

• Time Limit: 1s
• Memory Limit: 256MB

Sample Input 0

8
20 10 11 4 8 3 1 5
29 27 25 22 26 20 19 10

Sample Output 0

1 29
3 27
4 26
5 25
8 22
10 20
11 19
20 10

Sample Input 1

10
2 12 4 5 6 8 15 3 45 99
1 5 3 24 15 13 48 56 32 10

Sample Output 1

-1