Find Maximum Packages

Choose a single target total price T. Each bundle contains one or two products whose total price is T; each product can be used at most once, and some products may be left unused. Find the maximum number of bundles that can be formed.

输入格式

The first line contains n (1..200000), and the second line contains n prices (1..2000).

输出格式

Output one integer, the answer required by the problem.

样例 1

输入：

9
4 5 10 3 1 2 2 2 3

输出：

4

样例 2

输入：

3
2 2 2

输出：

3

样例 3

输入：

1
1

输出：

1

样例说明

Example 1: with target price 5 you can form [5], [4,1] and two [3,2], 4 bundles in total; enumerating other targets cannot give more. Example 2: with target price 2, each 2 forms its own bundle, 3 bundles in total, instead of forcing them into pairs. Example 3: the only product 1 forms a bundle by itself, so the answer is 1.