Problem Statement

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.

Input

The input is given from Standard Input in the following format:
N
$X_1 X_2 \ldots X_N$
$L_1 L_2 \ldots L_N$

Output

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

Constraints

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

Sample Input 1

3
-6 0 7
3 5 10

Sample Output 1

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

Sample Input 2

1
0
1000000000000000000

Sample Output 2

2000000000000000001

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

Sample Input 3

2
-100 100
1 1

Sample Output 3

0

No k satisfies the conditions.

见题面 Input 部分

见题面 Output 部分