Problem Statement

There are $N + 2$ tapis, numbered from $0$ to $N + 1$.

You will place all the tapis at integer coordinates on a number line. Multiple tapis may be placed at the same coordinate.

However, for each tapi $i(1 \leq i \leq N)$, the following conditions must be satisfied.

• The distance from tapi $i$ to tapi $0$ is at most $X_i$.
• The distance from tapi $i$ to tapi $N + 1$ is at most $Y_i$.

Tapi $0$ and tapi $N + 1$ are on bad terms. Therefore, find the maximum possible distance from tapi $0$ to tapi $N + 1$, along with an example of a placement of the tapis that achieves it.

Input

$N$
$X_1$ $X_2$ $\cdots$ $X_N$
$Y_1$ $Y_2$ $\cdots$ $Y_N$

• $1 \leq N \leq 2 \times 10^5$
• $0 \leq X_i, Y_i \leq 10^6$
• All inputs are integers.

Output

The output consists of $N + 3$ lines.

On the $1$st line, print the maximum distance from tapi $0$ to tapi $N + 1$.

On the following $N + 2$ lines, print the coordinates of the $N + 2$ tapis, one per line, in order starting from tapi $0$.

The coordinates of all tapis must be integers between $0$ and $10^{18}$, inclusive.

If there are multiple valid placements, you may print any of them.

Sample

2
1 10
2 1

3
0
1
2
3

3
0 0 0
0 0 0

0
3
3
3
3
3

3
50 20 1
40 30 1

2
2
35
15
1
0