Codeforces Round #FF 446A DZY Loves Sequences

预处理出每一个数字能够向后延伸多少，然后尝试将两段拼起来。

DZY has a sequence a, consisting of n integers.

We'll call a sequence ai, ai + 1, ..., aj (1 ≤ i ≤ j ≤ n) a subsegment of the sequence a. The value (j - i + 1) denotes the length of the subsegment.

Your task is to find the longest subsegment of a, such that it is possible to change at most one number (change one number to any integer you want) from the subsegment to make the subsegment strictly increasing.

You only need to output the length of the subsegment you find.

Input

The first line contains integer n (1 ≤ n ≤ 105). The next line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109).

Output

In a single line print the answer to the problem — the maximum length of the required subsegment.

Sample test(s)

input
6
7 2 3 1 5 6

output
5

Note

You can choose subsegment a2, a3, a4, a5, a6 and change its 3rd element (that is a4) to 4.

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;

int n,a[110000],dp[110000];

int main()
{
	scanf("%d",&n);
	for(int i=0;i<n;i++)
		scanf("%d",a+i);
	int nx=-1;
	for(int i=0;i<n;i++)
	{
		if(nx>i) 
		{
			dp[i]=nx-i;
			continue;
		}
		int j=i;
		while(j+1<n&&a[j]<a[j+1]) j++;
		dp[i]=j-i+1;
		nx=max(nx,j+1);
	}
	int ans=dp[0];
	for(int i=0;i<n;i++)
	{
		int p=dp[i]+i-1;
		if(p-1>=0&&p+1<n&&a[p+1]>a[p-1]+1)
		{
			ans=max(ans,dp[i]-1+dp[p+1]+1);
		}
		if(p+2<n&&a[p+2]>a[p]+1)
		{
			ans=max(ans,dp[i]+dp[p+2]+1);
		}
		if(p+1<n||i-1>=0) ans=max(ans,dp[i]+1);
		i=p;
	}
	printf("%d
",ans);
	return 0;
}