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D - Two Sequences

Score : $500$ points

Problem Statement

You are given two integer sequences, each of length $N$: $a_1, ..., a_N$ and $b_1, ..., b_N$.

There are $N^2$ ways to choose two integers $i$ and $j$ such that $1 \leq i, j \leq N$. For each of these $N^2$ pairs, we will compute $a_i + b_j$ and write it on a sheet of paper. That is, we will write $N^2$ integers in total.

Compute the XOR of these $N^2$ integers.

The XOR of integers $c_1, c_2, ..., c_m$ is defined as follows:

• Let the XOR be $X$. In the binary representation of $X$, the digit in the $2^k$'s place ($0 \leq k$; $k$ is an integer) is $1$ if there are an odd number of integers among $c_1, c_2, ...c_m$ whose binary representation has $1$ in the $2^k$'s place, and $0$ if that number is even.

For example, let us compute the XOR of $3$ and $5$. The binary representation of $3$ is $011$, and the binary representation of $5$ is $101$, thus the XOR has the binary representation $110$, that is, the XOR is $6$.

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Constraints

• All input values are integers.
• $1 \leq N \leq 200,000$
• $0 \leq a_i, b_i < 2^{28}$

Input

Input is given from Standard Input in the following format:

$N$

$a_1$ $a_2$ $...$ $a_N$

$b_1$ $b_2$ $...$ $b_N$

Output

Print the result of the computation.

2
1 2
3 4

2

On the sheet, the following four integers will be written: $4(1+3), 5(1+4), 5(2+3)$ and $6(2+4)$.

6
4 6 0 0 3 3
0 5 6 5 0 3

8

5
1 2 3 4 5
1 2 3 4 5

2

1
0
0

0