The Longest Spike

Choose any numbers from the array and rearrange them into a sequence that strictly increases and then strictly decreases. The two parts share the peak, and either part may consist of just the peak, so purely increasing, purely decreasing, and single-element sequences are also valid. Return the maximum length.

This site uses a standard input/output protocol.

输入格式

The first line contains N, and the second line contains N integers. This site uses 1≤N≤200000 and elements in −10⁹..10⁹.

输出格式

Output a single integer, the answer.

样例 1

输入：

2
1 2

输出：

2

样例 2

输入：

6
2 5 3 2 4 1

输出：

6

样例 3

输入：

3
5 5 5

输出：

1

样例说明

Example 1: 1, 2 is already a peak, of length 2. Example 2: you can arrange 1, 2, 3, 4, 5, 2, of length 6. Example 3: strictness forbids repeating the peak value, so only one 5 can be used.