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 $*x*_{1}, *x*_{2}, ..., *x*_{*n*}$. 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 $*y*_{1}, *y*_{2}, ..., *y*_{*n*}$. You should make $*x*_{1}, *x*_{2}, ..., *x*_{*n*}$ exactly equal to $*y*_{1}, *y*_{2}, ..., *y*_{*n*}$. 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: $*x*_{1}$ to $*x*_{*n*}$ $(0 ≤ *x*_{*i*} ≤ 10^{9})$. The third line contains $*n*$ integers: $*y*_{1}$ to $*y*_{*n*}$ $(0 ≤ *y*_{*i*} ≤ 10^{9})$.

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 $10^{6}$ operations.

Note

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