Hideo 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.
[samples]
Hideo Kojima 刚刚从 Konami 辞职。现在他需要找一份新工作。尽管他是一位广为人知的人物，但他仍然需要一份简历来申请职位。
在他整个职业生涯中，Hideo 制作了 #cf_span[n] 款游戏。其中一些是成功的，一些是失败的。Hideo 希望从他的简历中删除若干款游戏（可能为零款），以给雇主留下更好的印象。结果，他的简历中不应出现任何失败的游戏紧接在成功游戏之后的情况。
更正式地，你被给定一个由 0 和 1 组成的数组 #cf_span[s1, s2, ..., sn]。0 对应一个失败的游戏，1 对应一个成功的游戏。游戏按其被制作的顺序给出，Hideo 不能交换这些值。他应从该数组中删除某些元素，使得没有任何 0 紧接在 1 之后。
此外，Hideo 仍希望在他的简历中尽可能多地保留游戏。请帮助这位天才确定他最多可以保留多少款游戏。
第一行包含一个整数 #cf_span[n]（#cf_span[1 ≤ n ≤ 100]）。
第二行包含 #cf_span[n] 个用空格分隔的整数 #cf_span[s1, s2, ..., sn]（#cf_span[0 ≤ si ≤ 1]）。#cf_span[0] 对应一个失败的游戏，#cf_span[1] 对应一个成功的游戏。
请输出一个整数——Hideo 可以保留在简历中的最大游戏数量，使得没有任何失败的游戏出现在成功游戏之后。
## Input
第一行包含一个整数 #cf_span[n]（#cf_span[1 ≤ n ≤ 100]）。第二行包含 #cf_span[n] 个用空格分隔的整数 #cf_span[s1, s2, ..., sn]（#cf_span[0 ≤ si ≤ 1]）。#cf_span[0] 对应一个失败的游戏，#cf_span[1] 对应一个成功的游戏。
## Output
请输出一个整数——Hideo 可以保留在简历中的最大游戏数量，使得没有任何失败的游戏出现在成功游戏之后。
[samples]
Let $ s = [s_1, s_2, \dots, s_n] $ be a binary sequence where $ s_i \in \{0, 1\} $.
**Constraint:**
The resulting subsequence must not contain any occurrence of $ 1 $ immediately followed by $ 0 $, i.e., no substring "10".
**Objective:**
Maximize the length of a subsequence (not necessarily contiguous, but preserving order) of $ s $ satisfying the above constraint.
---
**Formal Problem Statement:**
Given a binary sequence $ s \in \{0,1\}^n $, find the maximum length of a subsequence $ s' $ of $ s $ such that there do not exist indices $ i < j $ in $ s' $ with $ s'_i = 1 $ and $ s'_j = 0 $.
---
**Equivalent Reformulation:**
The constraint "no 1 followed by 0" implies that in the resulting subsequence, all 0s must come before all 1s. That is, the subsequence must be of the form:
$$
\underbrace{0, 0, \dots, 0}_{a \text{ times}}, \underbrace{1, 1, \dots, 1}_{b \text{ times}}
$$
for some $ a, b \geq 0 $.
Thus, the problem reduces to:
Find the maximum value of $ a + b $, where $ a $ is the number of 0s selected from some prefix of $ s $, and $ b $ is the number of 1s selected from the corresponding suffix of $ s $, such that all selected 0s appear before all selected 1s in the original sequence.
---
**Optimization Strategy:**
For each possible split point $ k \in \{0, 1, \dots, n\} $, consider:
- Taking all 0s from positions $ 1 $ to $ k $,
- Taking all 1s from positions $ k+1 $ to $ n $.
Then the total length is:
$$
\text{count}_0(1..k) + \text{count}_1(k+1..n)
$$
The maximum over all $ k \in \{0, 1, \dots, n\} $ gives the answer.
---
**Final Mathematical Formulation:**
Let $ n \in \mathbb{N} $, $ s \in \{0,1\}^n $.
Define for $ k \in \{0, 1, \dots, n\} $:
$$
f(k) = \sum_{i=1}^{k} [s_i = 0] + \sum_{i=k+1}^{n} [s_i = 1]
$$
Then the answer is:
$$
\max_{k \in \{0, 1, \dots, n\}} f(k)
$$