There is an octopus-shaped robot and $N$ treasures on a number line. The $i$-th treasure $(1\leq i\leq N)$ is located at coordinate $X_i$.  
The robot has one head and $N$ legs, and the $i$-th leg $(1\leq i\leq N)$ has a length of $L_i$.

Find the number of integers $k$ such that the robot can grab all $N$ treasures as follows.

-   Place the head at coordinate $k$.
-   Repeat the following for $i=1,2,\ldots,N$ in this order: if there is a treasure that has not been grabbed yet within a distance of $L_i$ from the head, that is, at a coordinate $x$ satisfying $k-L_i\leq x\leq k+L_i$, choose one such treasure and grab it.

The input is given from Standard Input in the following format:

```
$N$
$X_1$ $X_2$ $\ldots$ $X_N$
$L_1$ $L_2$ $\ldots$ $L_N$
```

Print the number of integers $k$ that satisfy the condition in the statement.

-   $1 \leq N\leq 200$
-   $-10^{18} \leq X_1<X_2<\cdots<X_N\leq 10^{18}$
-   $1\leq L_1\leq L_2\leq\cdots\leq L_N\leq 10^{18}$
-   All input values are integers.

6

k=-3,-2,-1,2,3,4 satisfy the condition. For example, when k=-3, the robot can grab all three treasures as follows.

• The first leg can grab treasures at coordinates x satisfying -6≤x≤0. Among them, grab the first treasure at coordinate -6.
• The second leg can grab treasures at coordinates x satisfying -8≤x≤2. Among them, grab the second treasure at coordinate 0.
• The third leg can grab treasures at coordinates x satisfying -13≤x≤7. Among them, grab the third treasure at coordinate 7.

2000000000000000001

All integers k from $-10^{18}$ to $10^{18}$ satisfy the condition.

0

No k satisfies the conditions.