You are given an integer $K$, an integer sequence $A=(A_1,A_2,\ldots,A_N)$ of length $N$, and an integer sequence $B=(B_1,B_2,\ldots,B_M)$ of length $M$.

Find the number of pairs of $2$ integers $(p,q)$ that satisfy all of the following conditions:

• $1 \le p \le N$.
• $1 \le q \le M$.
• $A_p + K = B_q$.

Input

The input is given in the following format:

$$ \begin{aligned} &K \\ &N \\ &A_1 \ A_2 \ \cdots \ A_N \\ &M \\ &B_1 \ B_2 \ \cdots \ B_M \end{aligned} $$

Output

Output the number of pairs of $2$ integers $(p,q)$ that satisfy all the conditions.

Do not output anything other than the answer. (Do not output sentences prompting for input, etc.)

For the answer format, you may refer to the practice problems and their sample solutions.

Constraints

• $1 \le K \le 100$.
• $1 \le N \le 100$.
• $1 \le M \le 100$.
• $1 \le A_i \le 100$ ($1 \le i \le N$).
• $1 \le B_j \le 100$ ($1 \le j \le M$).
• All input values are integers.

Examples

Input 1

1
4
1 8 6 8
3
7 9 4

Output 1

3

Note 1

• Since $A_2 = 8, B_2 = 9$ and $A_2 + 1 = B_2$ holds, the pair of integers $(2,2)$ satisfies the conditions.
• Since $A_3 = 6, B_1 = 7$ and $A_3 + 1 = B_1$ holds, the pair of integers $(3,1)$ satisfies the conditions.
• Since $A_4 = 8, B_2 = 9$ and $A_4 + 1 = B_2$ holds, the pair of integers $(4,2)$ satisfies the conditions.

There are $3$ pairs of integers that satisfy the conditions: $(2,2),(3,1),(4,2)$. Therefore, output $3$.

Input 2

66
4
31 41 59 26
5
29 97 92 45 8

Output 2

2

Note 2

• Since $A_1 = 31, B_2 = 97$ and $A_1 + 66 = B_2$ holds, the pair of integers $(1,2)$ satisfies the conditions.
• Since $A_4 = 26, B_3 = 92$ and $A_4 + 66 = B_3$ holds, the pair of integers $(4,3)$ satisfies the conditions.

There are $2$ pairs of integers that satisfy the conditions: $(1,2),(4,3)$. Therefore, output $2$.

Input 3

99
5
1 1 1 1 1
6
100 100 100 100 100 100

Output 3

30

Note 3

• There are $30$ pairs of integers that satisfy the conditions. Therefore, output $30$.

Input 4

100
1
11
1
18

Output 4

0

Note 4

• There are no pairs of integers that satisfy the conditions. Therefore, output $0$.