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.io.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.StringTokenizer; 
import java.util.*;
 
public class Solution 
{ 
   
    public static void main(String[] args) throws IOException 
    { 
  
       BufferedReader br = new BufferedReader( 
                              new InputStreamReader(System.in));
        StringBuilder out=new StringBuilder(); 
            int n=Integer.parseInt(br.readLine());
           StringTokenizer  st=new StringTokenizer(br.readLine());
           int arr[]=new int[n];
      for(int j=0;j<n;j++){

            arr[j]=Integer.parseInt(st.nextToken());
      }
        int l[]=new int[n];
        int r[]=new int[n];
        l[0]=1;
        r[n-1]=1;
        int max=Integer.MIN_VALUE;
        for(int i=1;i<n;i++){
            if(arr[i]>arr[i-1])
            l[i]=l[i-1]+1;
            else
            l[i]=1;
            max=Math.max(max,l[i]);
        }
          for(int i=n-2;i>=0;i--){
            if(arr[i]<arr[i+1])
            r[i]=r[i+1]+1;
            else
            r[i]=1;
            max=Math.max(max,r[i]);
        }
        
         for(int i=0;i<n-2;i++){
             if(arr[i]<arr[i+2])
             max=Math.max(max,l[i]+r[i+2]);
         }
      
      System.out.println(max);
    }
}
 class Segment{
    int s;
    int e;
    public Segment(int x,int y){
        s=x;
        e=y;
    }
     
 }
class SortSeg implements Comparator<Segment> 
{ 
    // Used for sorting in ascending order of 
    // roll number 
    public int compare(Segment a, Segment b) 
    { 
        int lena= a.e-a.s+1;
         int lenb= b.e-b.s+1;
        if(lena==lenb)
        return a.s - b.s; 
        else
        //decsending order
        return lenb-lena;
    } 
}