You are given an array a consisting of n integers.

You can remove at most one element from this array. Thus, the final length of the array is n-1 or n.

Your task is to calculate the maximum possible length of the strictly increasing contiguous subarray of the remaining array.

Recall that the contiguous subarray a with indices from l to r is a[l ... r] = a_l, a_{l + 1}, ..., a_r. The subarray a[l ... r] is called strictly increasing if a_l < a_{l+1} < ... < a_r.

Input

The first line of the input contains one integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of elements in a.

The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9), where a_i is the i-th element of a.

Output

Print one integer — the maximum possible length of the strictly increasing contiguous subarray of the array a after removing at most one element.

Examples

Input


5
1 2 5 3 4


Output


4


Input


2
1 2


Output


2


Input


7
6 5 4 3 2 4 3


Output


2

Note

In the first example, you can delete a_3=5. Then the resulting array will be equal to [1, 2, 3, 4] and the length of its largest increasing subarray will be equal to 4.

import java.util.*;
import java.io.*;
import java.util.Scanner;
import java.util.*;
 
 public class bfs 
{ 
	static int fun(int[] nums, int n) 
	{ 
		int ans =1;
		int []aa=new int[n];
		Arrays.fill(aa, 1);
		int []bb=new int[n];
		Arrays.fill(bb, 1);

		
		for( int i=1;i<n;i++) {
			if(nums[i-1]<nums[i]) aa[i]=aa[i-1]+1;
			ans=Math.max(aa[i], ans);
		}
		
		
		for( int i=n-2;i>=0;i--) {
			if(nums[i]<nums[i+1]) bb[i]=bb[i+1]+1;
		}
		
		int temp=1;
//		for(Integer gg:aa) System.out.println(gg);
//		for(Integer gg:bb) System.out.println(gg+" dd");
//		
		for( int i=0;i<n-2;i++) {
			if (nums[i] < nums[i + 2]) 
			temp=Math.max(aa[i], aa[i]+bb[i+2]);
	//		System.out.println("vs"+aa[i]+" "+bb[i+2]);
			ans=Math.max(ans, temp);
		}
		
		return ans;
		
	} 

	public static void main(String[] args) throws IOException
	{ 
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));


		int n=Integer.parseInt(reader.readLine());
		String[] temp=reader.readLine().split(" ");
		int[] a=new int[n];
		int i=0;
		for(String h:temp) a[i++]=Integer.parseInt(h);

		System.out.println(fun(a, n)); 
	} 
}