P4 - HEIGHT

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Points: 10 (partial)
Time limit: 1.0s
Memory limit: 32M

Authors:
Problem type
Allowed languages
Ada, Assembly, Awk, Brain****, C, C#, C++, COBOL, CommonLisp, D, Dart, F#, Forth, Fortran, Go, Groovy, Haskell, Intercal, Java, JS, Kotlin, Lisp, Lua, Nim, ObjC, OCaml, Octave, Pascal, Perl, PHP, Pike, Prolog, Python, Racket, Ruby, Rust, Scala, Scheme, Sed, Swift, TCL, Text, Turing, VB, Zig

Mr.Hsiung dresses fashionably everyday. Not surprisingly, he only does this because he is overly conscious about his height. He has a sequence of integers, each representing his height at a certain time. However, he organized them poorly. Mr.Hsiung doesn't care about having all of the heights, so he will take some of them, while keeping their relative order. Additionally, this new subsequence of numbers he has must be strictly increasing, as it wouldn't make sense for him to grow shorter. He also wants the sequence with the sum of its elements being maximal. Help Mr.Hsiung find this sum.

Input Specification

The first line contains the integer , the number of elements in the original sequence. The lines will contain elements, a positive integer at most . For % of test cases, .

Output Specification

Output the maximum sum of Mr.Hsiung's new sequence.

Sample Input 1

5
4
1
2
5
6

Sample Output 1

15

Explanation 1

In this case, the subsequence is optimal.

Sample Input 2

5
10
9
8
7
6

Sample Output 2

10

Explanation 2

In this case, no subsequence containing more than 1 element is increasing. Thus, choosing is optimal.