【CF Edu 28 A. Curriculum Vitae】

time limit per test 1 second

memory limit per test 256 megabytes

input standard input

output standard output

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 s₁, s₂, ..., 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 s₁, s₂, ..., 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

【翻译】给出一个长度为n的01序列，现在可以删除一些数，使得最终序列满足对于任何一个1后面所有位置都不会有0，求剩余元素个数的最大值。

题解：

     ①根据题目，可以的枚举哪个地方开始选择1，那么之后的0都要删除。

     ②实现方法是分别维护0和1的前缀，然后O(n)扫一遍就可以了。

#include<stdio.h>
#include<algorithm>
#define go(i,a,b) for(int i=a;i<=b;i++)
using namespace std;int n,ans,t,a[2][102];
int main()
{
	scanf("%d",&n);
	go(i,1,n)scanf("%d",&t),a[0][i]=a[0][i-1],a[1][i]=a[1][i-1],a[t][i]++;
	go(i,1,n)if(a[1][i]!=a[1][i-1])ans=max(ans,a[0][i]+a[1][n]-a[1][i-1]);
	ans=max(ans,a[0][n]);printf("%d\n",ans);
	return 0;
}//Paul_Guderian

这是1999年的冬天,从来没经历过的寒冷,

街边的楼群指着蓝天,人们都蜷缩在大衣里行色匆匆。——————汪峰《再见二十世纪》