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A. Curriculum Vitae

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputHideo Kojima has just quit his job at Konami. Now he is going to find a new place to work. Despite being such a well-known person, he still needs a CV to apply for a job.

During all his career Hideo has produced *n* games. Some of them were successful, some were not. Hideo wants to remove several of them (possibly zero) from his CV to make a better impression on employers. As a result there should be no unsuccessful game which comes right after successful one in his CV.

More formally, you are given an array *s*_{1}, *s*_{2}, ..., *s*_{n} of zeros and ones. Zero corresponds to an unsuccessful game, one — to a successful one. Games are given in order they were produced, and Hideo can't swap these values. He should remove some elements from this array in such a way that no zero comes right after one.

Besides that, Hideo still wants to mention as much games in his CV as possible. Help this genius of a man determine the maximum number of games he can leave in his CV.

Input

The first line contains one integer number *n* (1 ≤ *n* ≤ 100).

The second line contains *n* space-separated integer numbers *s*_{1}, *s*_{2}, ..., *s*_{n} (0 ≤ *s*_{i} ≤ 1). 0 corresponds to an unsuccessful game, 1 — to a successful one.

Output

Print one integer — the maximum number of games Hideo can leave in his CV so that no unsuccessful game comes after a successful one.

Examples

Input

4

1 1 0 1

Output

3

Input

6

0 1 0 0 1 0

Output

4

Input

1

0

Output

1

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

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