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Longest Bitonic Subsequence

1. You are given a number n, representing the number of elements. 2. You are given n numbers, representing the contents of array of length n. 3. You are required to print the length of longest bitonic subsequence of array. Note -> bitonic subsequence begins with elements in increasing order, followed by elements in decreasing order.

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Longest Bitonic Subsequence

easy

1. You are given a number n, representing the number of elements. 2. You are given n numbers, representing the contents of array of length n. 3. You are required to print the length of longest bitonic subsequence of array. Note -> bitonic subsequence begins with elements in increasing order, followed by elements in decreasing order.

Constraints

0 <= n <= 20 0 <= n1, n2, .. <= 100

Format

Input

A number n .. n more elements

Output

A number representing the length of longest increasing subsequence of array.

Example

Sample Input

10 10 22 9 33 21 50 41 60 80 1

Sample Output

7

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