There are some tasks which have the following structure: you are given a model, and you can do some operations, you should use these operations to achive the goal. One way to create a new task is to use the same model and same operations, but change the goal.

Let's have a try. I have created the following task for Topcoder SRM 557 Div1-Hard: you are given n integers x₁, x₂, ..., x_n. You are allowed to perform the assignments (as many as you want) of the following form x_i ^= x_j (in the original task i and j must be different, but in this task we allow i to equal j). The goal is to maximize the sum of all x_i.

Now we just change the goal. You are also given n integers y₁, y₂, ..., y_n. You should make x₁, x₂, ..., x_n exactly equal to y₁, y₂, ..., y_n. In other words, for each i number x_i should be equal to y_i.

Input

The first line contains an integer n (1 ≤ n ≤ 10000). The second line contains n integers: x₁ to x_n (0 ≤ x_i ≤ 10⁹). The third line contains n integers: y₁ to y_n (0 ≤ y_i ≤ 10⁹).

Output

If there is no solution, output -1.

If there is a solution, then in the first line output an integer m (0 ≤ m ≤ 1000000) – the number of assignments you need to perform. Then print m lines, each line should contain two integers i and j (1 ≤ i, j ≤ n), which denote assignment x_i ^= x_j.

If there are multiple solutions you can print any of them. We can prove that under these constraints if there exists a solution then there always exists a solution with no more than 10⁶ operations.

Note

Assignment a ^= b denotes assignment a = a ^ b, where operation "^" is bitwise XOR of two integers.

Design Tutorial: Change the Goal

Examples