Sum of pairs

Problem code: PAIRSUM

All submissions for this problem are available.

We call an array of integers X of size N good if it can be partitioned into 2 arrays of size n/2, say p1[ ] and p2[ ], such that p1[0] + p2[0] = p1[1] + p2[1] = p1[2] + p2[2] = ... . Given an array Y, determine the size of its largest subset which is a good array.

Input

The first line contains the integer N (≤ 100). The next line contains N space separated integers, which are the elements of the array X.

Output

One number which is the size of the greatest subset as mentioned in the problem statement.

Example

Input:
6

1 4 2 3 8 10 
Output:
4
Explanation:
The array {1,4,2,3} is good, since you can form p1[] = {1,2} and p2[] = {4,3}. (satisfying 1 + 4 = 2 + 3)

Date:	2009-07-21
Time limit:	1s
Source limit:	50000B
Languages:	All except: TCL ERL
Resource:	syco

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