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.*;
import java.lang.*;

public class Main {

    public static void main(String[] args) throws IOException {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        int n=Integer.parseInt(br.readLine());

        String s = br.readLine();
        String[] s1 = s.split(" ");
        int[] arr = new int[n];

        for(int i=0;i<n;i++)
        {
            arr[i]=Integer.parseInt(s1[i]);
        }

        int max=0,count=1,i=0,first=0;
        boolean rev=false;

        while(true){

            if(i==n-1){
                if(count>max)
                    max=count;

                break;
            }

            if(arr[i+1]>arr[i]){
                count++;
            }

            else if(arr[i+1]<=arr[i] && !rev){
                first=i+1;
                rev=true;

                if(i+2<=n-1 && arr[i+2]>arr[i]){
                    count++;
                    i=i+1;
                }else{
                    rev=false;
                    i=first;

                    if(count>max)
                        max=count;

                    count=1;

                    continue;
                }
            }

            else if(arr[i+1]<=arr[i] && rev){
               rev=false;
               i=first;

               if(count>max)
                   max=count;

               count=1;

               continue;
            }

            if(i==n-1){
                if(count>max)
                    max=count;

                break;
            }

            i++;

            if(i==n-1){
                if(count>max)
                    max=count;

                break;
            }

        }

        i=0;
        count=1;
        rev=false;
        first=0;

        while(true){

            if(i==n-1){
                if(count>max)
                    max=count;

                break;
            }

            if(arr[i+1]>arr[i]){
                count++;
            }

            if(arr[i+1]<arr[i] && !rev){

                rev=true;
                first=i+1;

                if(i-1>=0 && i+1<=n-1 && arr[i+1]>arr[i-1]){

                }else{
                    rev=false;
                    i=first;

                    if(count>max)
                        max=count;

                    count=1;

                    continue;
                }
            }

            else if(arr[i+1]<=arr[i] && rev){
                rev=false;
                i=first;

                if(count>max)
                    max=count;

                count=1;

                continue;
            }


            if(i==n-1){
                if(count>max)
                    max=count;

                break;
            }

            i++;

            if(i==n-1){
                if(count>max)
                    max=count;

                break;
            }
        }

        System.out.println(max);

    }
}
