&+ +&

Two positive integer sequences of length $N$ are given: $A_1, A_2, \dots, A_N$ and $B_1, B_2, \dots, B_N$. For every ordered pair $(i, j)$ with $1 \le i \le N$ and $1 \le j \le N$, compute the following two values.

• The remainder of the sum of all $(A_i \mathbin{\&} B_j)$ divided by $1999$
• The bitwise AND of all $(A_i + B_j)$ values

$\mathbin{\&}$ is bitwise AND. Its definition is in the Hint section.

The first line gives the sequence length $N$ ($1 \le N \le 10^6$). The second line gives $N$ integers of sequence $A$, separated by spaces, and the third line gives $N$ integers of sequence $B$, separated by spaces. Every element of $A$ and $B$ is a positive integer with $1 \le A_i, B_i \le 2^{28}$.

Print the two values described above on the first line, separated by a space, in order.

Bitwise AND applies to each binary digit. Write both operands in binary first, then set a digit to $1$ only when both operands have $1$ there, and to $0$ otherwise.

As an illustration, $13 \mathbin{\&} 7 = 5$. Here $13$ is $1101_2$ in binary and $7$ is $111_2$. After aligning digits to $1101_2$ and $0111_2$, the digitwise AND is $0101_2$, which equals $5$ in decimal.