What came first, the chicken or the egg? Is it better to live a hundred years as a millionaire or seven days in poverty? How to become a chess grandmaster? How to raise blinds? How to pass the final exams? How to train a dragon? These are interesting questions we can ponder only after the competition, but now we offer one less interesting computer science problem.

You are given two sets of numbers ~A~ and ~B~ of size ~N~. In one move, you can select an arbitrary element from set ~A~ and change one arbitrary digit (bit) in its binary representation. The resulting number must not be an element of set ~A~ immediately before the change.

For example, the number ~5~ in binary is ~0101_2~. In one move, it can become ~13 = 1101_2~, ~1 = 0001_2~, ~7 = 0111_2~, or ~4 = 0100_2~ if we change its 4th, 3rd, 2nd, or 1st bit, respectively.

Determine a sequence of moves by which set ~A~ becomes equal to set ~B~. Sets are equal if they have the same size and there is no element in set ~A~ that does not belong to set ~B~.

Note: The number of moves does not have to be minimal, but it must satisfy the task constraints.

Input Specification

The first line contains the integer ~N~ ~(1 \le N \le 2^{15})~, the size of the sets ~A~ and ~B~.

The second line contains ~N~ distinct integers ~a_i~ ~(0 \le a_i < 2^{15})~, the elements of the set ~A~.

The third line contains ~N~ distinct integers ~b_i~ ~(0 \le b_i < 2^{15})~, the elements of the set ~B~.

Output Specification

In the first line, print the number of required moves.

In the remaining lines, print the numbers ~x~ and ~y~ ~(0 \le x, y < 2^{15})~ — we change the number ~x~ from set ~A~ to the number ~y~. The numbers ~x~ and ~y~ must differ by exactly one bit, and ~x \in A~ and ~y \notin A~ must hold at the moment we execute the move.

The number of moves you make must not exceed ~2^{19}~. It can be shown that a solution always exists within the given constraints.

Constraints

Subtask	Points	Constraints
1	10	~a_i, b_i \le 2^{14}~
2	15	~N \le 7~
3	30	~N \le 27~
4	15	No additional constraints.

Sample Input 1

3
0 1 2
1 2 3

Sample Output 1

2
1 3
0 1

Explanation for Sample 1

If we first make the move 0 1, and then 1 3, between these two moves, set ~A~ would have two identical elements, which the task does not allow. A possible solution is 2 3, 0 2.

Sample Input 2

3
4 8 31
0 4 8

Sample Output 2

5
31 30
30 28
28 24
24 16
16 0

Explanation for Sample 2

~31 = 11111_2~. By removing bits from least to most significant, we obtain the numbers ~30~, ~28~, ~24~, ~16~, and ~0~ in sequence. After all moves, set ~A~ becomes equal to set ~B~.

Sample Input 3

5
0 1 2 4 5
7 6 5 3 2

Sample Output 3

9
1 3
3 7
0 1
1 0
2 6
0 2
7 3
5 7
4 5