BeginnerHashmap3000 ms256 MB

Two Summer

Given a number n and a list A of size n provide the count of all pairs that add up to every number in list B of size n.

Statement

Given a number n and a list A of size n provide the count of all pairs that add up to every number in list B of size n.

Input

n, 2 integer lists of size n

Output

1 integer list of size n

Constraints

  • 1 <=n <=800

Examples

Example 1

Input

6
4 9 -1 0 -3 1
2 4 0 9 -4 1

Output

0
1
1
1
1
2

For 2, there is no possible pairs of numbers in A that add of to 2, then for 4,0,9,and -4, there is only one possible pair to add of to those numbers, (0,4)=4, (-1,1)=0,(9,0)=9,(-1,-3)=-4, and for 1, both (4,-3)=1, and (0,1)=1, so 2 possible pairs add up to 1.

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