You are given a playlist of a radio station since its establishment. The playlist has a total of $n$ songs.

What is the longest sequence of successive songs where each song is unique?

Input

The first input line contains an integer $n$: the number of songs.

The next line has $n$ integers $k_1,k_2,\ldots,k_n$: the id number of each song.

Output

Print the length of the longest sequence of unique songs.

Constraints

• $1 \le n \le 2 \cdot 10^5$
• $1 \le k_i \le 10^9$

Example

Input:

8
1 2 1 3 2 7 4 2

Output:

5