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C. Swap Letters

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputMonocarp has got two strings $$$s$$$ and $$$t$$$ having equal length. Both strings consist of lowercase Latin letters "a" and "b".

Monocarp wants to make these two strings $$$s$$$ and $$$t$$$ equal to each other. He can do the following operation any number of times: choose an index $$$pos_1$$$ in the string $$$s$$$, choose an index $$$pos_2$$$ in the string $$$t$$$, and swap $$$s_{pos_1}$$$ with $$$t_{pos_2}$$$.

You have to determine the minimum number of operations Monocarp has to perform to make $$$s$$$ and $$$t$$$ equal, and print any optimal sequence of operations — or say that it is impossible to make these strings equal.

Input

The first line contains one integer $$$n$$$ $$$(1 \le n \le 2 \cdot 10^{5})$$$ — the length of $$$s$$$ and $$$t$$$.

The second line contains one string $$$s$$$ consisting of $$$n$$$ characters "a" and "b".

The third line contains one string $$$t$$$ consisting of $$$n$$$ characters "a" and "b".

Output

If it is impossible to make these strings equal, print $$$-1$$$.

Otherwise, in the first line print $$$k$$$ — the minimum number of operations required to make the strings equal. In each of the next $$$k$$$ lines print two integers — the index in the string $$$s$$$ and the index in the string $$$t$$$ that should be used in the corresponding swap operation.

Examples

Input

4 abab aabb

Output

2 3 3 3 2

Input

1 a b

Output

-1

Input

8 babbaabb abababaa

Output

3 2 6 1 3 7 8

Note

In the first example two operations are enough. For example, you can swap the third letter in $$$s$$$ with the third letter in $$$t$$$. Then $$$s = $$$ "abbb", $$$t = $$$ "aaab". Then swap the third letter in $$$s$$$ and the second letter in $$$t$$$. Then both $$$s$$$ and $$$t$$$ are equal to "abab".

In the second example it's impossible to make two strings equal.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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