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.
/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Ideone
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
      Scanner sc = new Scanner(System.in);
        int n=sc.nextInt();
        int[] a=new int[n];

        for(int i=0;i<n;i++)
            a[i]=sc.nextInt();

        int[] pref=new int[n];
        Arrays.fill(pref,1);

        int[] suff=new int[n];
        Arrays.fill(suff,1);

        int max=1;

        for(int i=1;i<n;i++)
        {
            if(a[i]>a[i-1])
                pref[i]=pref[i-1]+1;
            else
                pref[i]=1;
        }

        for(int i=n-2;i>=0;i--)
        {
            if(a[i+1]>a[i])
                suff[i]=suff[i+1]+1;
            else
                suff[i]=1;
        }

        for(int i=1;i<n-1;i++)
        {
            if(a[i+1]>a[i-1])
            max=Math.max(max,pref[i-1]+suff[i+1]);
        }
        for(int i=0;i<n;i++)
        {
            max=Math.max(max,Math.max(pref[i],suff[i]));
        }

        System.out.println(max);
       
    }
}