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# Problem ESquare Peg in a Round Hole

Mr. Johnson likes to build houses. In fact, he likes it so much that he has built a lot of houses that he has not yet placed on plots. He has recently acquired $N$ circular plots. The city government has decided that there can be only one house on each plot, and a house cannot touch the boundary of the plot.

Mr. Johnson has $M$ circular houses and $K$ square houses. Help him figure out how many of the plots he can fill with houses so that he can get some money back on his investments.

## Input

The first line of input consists of $3$ space-separated integers $N$, $M$, and $K$. The second line contains $N$ space-separated integers, where the $i^{\text {th}}$ integer denotes the radius $r_ i$ of the $i^{\text {th}}$ plot. The third line contains $M$ space-separated integers, where the $i^{\text {th}}$ integer denotes the radius $r_ i$ of the $i^{\text {th}}$ circular house. The fourth line contains $K$ space-separated integers, where the $i^{\text {th}}$ integer denotes the side length $s_ i$ of the $i^{\text {th}}$ square house.

## Output

Output the largest number of plots he can fill with houses.

## Limits

• $1 \leq N, M, K, r_ i, s_ i \leq 100$

Sample Input 1 Sample Output 1
5 3 3
1 2 6 7 8
2 6 7
4 8 9

3

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