Get Minimum Number of Unique Distribution Centers

On day i, choose a center numbered 1..n. If demand is higher than on the previous day, the center number must be strictly higher; if demand is lower, it must be strictly lower; if demand is equal, the same center must be used. Minimize the number of distinct centers used over all days.

输入格式

The first line contains n; the second line contains each day's demand. The original text had no numeric bounds; this site uses 1≤n≤200000, 0≤demand≤10^9.

输出格式

Output a single integer, the answer.

样例 1

输入：

5
10 20 30 15 10

输出：

3

样例 2

输入：

4
1 2 2 3

输出：

3

样例 3

输入：

2
5 5

输出：

1

样例说明

The answers are 3, 3 and 1. Equal demands do not interrupt a continuing rising constraint.