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.*;
public class RemoveOneElement {
    public static void main(String args[]){
        Scanner sc= new Scanner(System.in);
        int n=sc.nextInt();
        int a[]=new int[n];
        int l[]=new int[n];
        int r[]=new int[n];
        for(int i=0;i<n;i++){
            a[i]=sc.nextInt();
            l[i]=1;
            r[i]=1;
        }
        
        for(int i=1;i<n;i++){
            if(a[i]>a[i-1])
                l[i]=l[i-1]+1;
        }
        for(int i=n-2;i>=0;i--){
            if(a[i]<a[i+1])
                r[i]=r[i+1]+1;
        }
        int re[]=new int[n];
        int x;
        for(int i=0;i<n;i++){
            re[i]=Math.max(l[i], r[i]);
        }
        for(int i=1;i<n-1;i++){
            if(a[i-1]<a[i+1]){
                x=l[i-1]+r[i+1];
                if(x>re[i])
                    re[i]=x;
            }
        }
        int ans=Integer.MIN_VALUE;
        for(int i=0;i<n;i++){
            if(re[i]>ans)
                ans=re[i];
        }
        System.out.println(ans);
    }
}
