Given an array of n integers, you are asked to find the longest increasing subsequence of the array. If there are multiple such subsequences you can output any of them.

A subsequence of an array is obtained by deleting some (possibly zero) elements of the array, without changing the order of the remaining elements. For example, if the array is , then is a subsequence of , but is not a subsequence of , since the order of the elements is not preserved.

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An increasing subsequence of an array is a subsequence in which the elements are in increasing order. For example, if the array is , then is an increasing subsequence of , but is not an increasing subsequence of , since the elements are not in increasing order.

Input

The first line of the input contains a single integer n (1 β€ n β€ 100 000), the length of the array.

The second line contains n space-separated integers (), representing the elements of the array.

Output

The program should print the length of the longest increasing subsequence of the array.

Examples

Input

Output

8
1 3 2 4 5 2 6 5

5

6
10 9 2 5 3 7

3

Explanation

In the first example, the longest increasing subsequence of the array is .

In the second example, the longest increasing subsequence of the array is .