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.*;

public class RemoveOneElement{
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long a[] = new long[n+1];
        for(int i=1;i<=n;i++)
            a[i] = sc.nextLong();
        ArrayList<Combine> arrayList = new ArrayList<>();
        long max = a[1];
        int start = 1;
        int end = 1;
        for(int i=2;i<=n;i++){
            if(a[i]<=a[i-1]){
                end = i-1;
                arrayList.add(new Combine(start , end));
                start = i;
            }
        }
        arrayList.add(new Combine(start , n));
        // for(int i=0;i<arrayList.size();i++){
        //     System.out.println(arrayList.get(i).start + " " + arrayList.get(i).end);
        // }
        int max1 = 0 , gMax = 0;
        for(int i=0;i<arrayList.size()-1;i++){
            Combine c = arrayList.get(i);
            Combine d = arrayList.get(i+1);
            max1 = c.end - c.start+1;
            int max2 = 0, max3 = 0;
            try{
                if(a[c.end-1]<a[d.start]){
                    max2 = d.end - c.start;
                }
            }
            catch(Exception e){

            }
            try{
                if(a[c.end]<a[d.start+1]){
                    max3 = d.end - c.start;
                }
            }
            catch(Exception e){

            }
            int j = Math.max(max1 , Math.max(max2 , max3));
            if(gMax<j)
                gMax = j;
        }
        Combine c = arrayList.get(arrayList.size()-1);
        if(gMax<c.end-c.start+1){
            gMax = c.end - c.start+1;
        }
        System.out.println(gMax);
    }
}

class Combine{
    int start,end;
    Combine(int start , int end){
        this.start = start;
        this.end = end;
    }
}
