Get Exp.

Repeatedly take the two people with the highest and the lowest remaining experience, pair them and remove them; count the distinct values among the pairs' average experience. People with the same experience are still separate individuals.

输入格式

The first line contains an even n; the second line contains n experience values. 2≤n≤100000, 0≤experience≤10^9.

输出格式

Output a single integer, the answer.

样例 1

输入：

6
1 4 1 3 5 6

输出：

2

样例 2

输入：

2
0 0

输出：

1

样例 3

输入：

4
1 100 10 1000

输出：

2

样例说明

The answers are 2, 1 and 2; the sums in the first example are 7, 6 and 7.