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

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

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