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 ≤ n ≤ 1000), 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 .