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Problem 4990. -- [Usaco2017 Feb]Why Did the Cow Cross the Road II

4990: [Usaco2017 Feb]Why Did the Cow Cross the Road II

Time Limit: 10 Sec  Memory Limit: 128 MB
Submit: 209  Solved: 130
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Description

Farmer John is continuing to ponder the issue of cows crossing the road through his farm, introduced
 in the preceding problem. He realizes that interaction between some pairs of breeds is actually acc
eptable if the breeds are friendly, a property that turns out to be easily characterized in terms of
 breed ID: breeds aa and bb are friendly if |a-b|≤4, and unfriendly otherwise. It is ok for cows to
 wander into fields designated for other breeds, as long as they are friendly.Given the ordering of 
N fields on both sides of the road through FJ's farm (again, with exactly one field for each breed o
n each side), please help FJ determine the maximum number of crosswalks he can draw over his road, s
uch that no two intersect, and such that each crosswalk joins a pair of fields containing two breeds
 that are friendly. Each field can be accessible via at most one crosswalk (so crosswalks don't meet
 at their endpoints).
上下有两个长度为n、位置对应的序列A、B,
其中数的范围均为1~n。若abs(A[i]-B[j]) <= 4,
则A[i]与B[j]间可以连一条边。现要求在边与边不相交的情况下的最大的连边数量。
n <= 10^6

Input

The first line of input contains N (1≤N≤100,0000). 
The next N lines describe the order, by breed ID, of fields on one side of the road; 
each breed ID is an integer in the range 1…N 
The last N lines describe the order, by breed ID, of the fields on the other side of the road. 
Each breed ID appears exactly once in each ordering.
注意:两个序列都是全排列

Output

Please output the maximum number of disjoint "friendly crosswalks" Farmer John can draw across the road.

Sample Input

6
1
2
3
4
5
6
6
5
4
3
2
1

Sample Output

5

HINT

Source

Platinum

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