Playlist

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