Bitovi

문제

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 $4$ th, $3$ rd, $2$ nd, or $1$ st 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.

입력

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

The second line contains $N$ different integers $a_{i}$ ( $0 ≤ a_i < 2^{15}$ ), the elements of the set $A$ .

The third line contains $N$ different integers $b_{i}$ ( $0 ≤ b_i < 2^{15}$ ), the elements of the set $B$ .

출력

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

In the remaining lines, print the numbers $x$ and $y$ ( $0 ≤ x, y < 2^{15}$ ) – 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 $y \not\in A$ must hold at the moment we execute the move.

문제

입력

출력

예제

예제 1

예제 2

예제 3