## SBO - MAXIMUM RARITY

Given a sequence of numbers, each number between 1 and 100000 (inclusive), find the contiguous subsequence with maximum rarity.

The rarity of a sequence is defined as the count of numbers which appear only once in that sequence. For example, let's consider the following sequence:

1 1 2 5 1 16 5

The rarity of the subsequence 1 1 2 5 is 2. This is because 2 and 5 are the only numbers which appear just once. 1 appears twice in the sequence, hence doesn't contribute to it's rarity. The rarity of subsequence 1 16 5 is 3 as each of the numbers appears only once. The maximum rarity achieved by any contiguous subsequence in the sequence 1 1 2 5 1 16 5 is 4. This is the rarity of 2 5 1 16.

Your task is to find the contiguous subsequence with maximum rarity and output that rarity value. You don't have to output the subsequence itself.

### Input

The first line of input will contain an integer N. N is the count of numbers in the input sequence.

1<=N<=500000.

The next line will contain the sequence of numbers. Each number in the sequence is an integer between 1 and 100000.

### Output

The maximum rarity that any contiguous subsequence possesses.

### Example

```Input 1:
71 1 2 5 1 16 5Output 1:
4Input 2:31 2 3Output 2:3Input 3:102 1 4 1 5 6 7 1 8 2Output 3:6Input 4:203 4 14 14 9 7 11 7 15 13 9 9 14 9 13 10 13 9 5 4Output 4:7Explanation:Input 2: The maximum rarity is achieved by the sequence itself.Input 3: The maximum rarity is achieved by the subsequences 1 4 1 5 6 7 1 8 2, 4 1 5 6 7 1 8 2 and 5 6 7 1 8 2.            All the three contiguous subsequences have rarity 6.Input 4: The maximum rarity is achieved by the subsequence 11 7 15 13 9 9 14 9 13 10 13 9 5 4.            This sequence has 7 numbers which appear only once in it, i.e., 11, 7, 15, 14, 10, 5, 4.```