Problem Statement

The magician Koa has flowers of $N$ colors numbered $1, 2, \dots, N$, with $A_{1}, A_{2}, \dots, A_{N}$ flowers of each color, respectively.

Koa performs the following operation on them any number of times, $0$ or more.

• Choose $1$ integer $i$ between $1$ and $N$, inclusive, and do the following.

• If Koa has at least $1$ flower of color $C_{i}$, change the color of any $1$ of those flowers to color $i$ by magic.

After finishing all of the above operations, Koa performs the following operation $0$ or more times, for as long as possible.

• Use $B_{1}, B_{2}, \dots, B_{N}$ flowers of colors $1, 2, \dots, N$, respectively, to make $1$ bouquet.
  However, the same flower cannot be used for multiple bouquets.

What is the maximum number of bouquets Koa can make?

Constraints

• $1 \leq N \leq 10^{5}$

• $0 \leq A_{i}, B_{i} \leq 10^{9}$ $(1 \leq i \leq N)$

• The sum of $B_{1}, B_{2}, \dots, B_{N}$ is at least $1$

• $1 \leq C_{i} \leq N$ $(1 \leq i \leq N)$

• All input values are integers

Input

The input is given in the following format.

$N$
$A_{1}$ $A_{2}$ $\cdots$ $A_{N}$
$B_{1}$ $B_{2}$ $\cdots$ $B_{N}$
$C_{1}$ $C_{2}$ $\cdots$ $C_{N}$

• Line $1$ contains $N$

• Line $2$ contains $A_{1}, A_{2}, \dots, A_{N}$ in this order, separated by single-byte spaces

• Line $3$ contains $B_{1}, B_{2}, \dots, B_{N}$ in this order, separated by single-byte spaces

• Line $4$ contains $C_{1}, C_{2}, \dots, C_{N}$ in this order, separated by single-byte spaces

Output

Print the answer on $1$ line.

Sample

3
9 3 1
1 2 3
2 1 1

2

2
0 100
100 0
1 1

0

12
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000
0 0 0 0 0 0 0 0 0 0 0 1
2 3 4 5 6 7 8 9 10 11 12 1

12000000000