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.Scanner;

public class Main {
    static int[][][] aa;
    static int maxx(int[] arr,int ind,int flag,int flag1){
        if(ind>=arr.length){
            return 0;
        }
        if(aa[ind][flag][flag1]!=-1){
            return aa[ind][flag][flag1];
        }
        if(flag==0){
            return aa[ind][flag][flag1]= Math.max(maxx(arr,ind+1,1,0)+1,maxx(arr,ind+1,0,0));

        }else if(flag==1){

                if(arr[ind]>arr[ind-1]){
                    return aa[ind][flag][flag1]= Math.max( maxx(arr,ind+1,1,0)+1,maxx(arr,ind+1,2,1) );
                }else{
                    return  aa[ind][flag][flag1]=maxx(arr,ind+1,2,1);
                }
        }else if(flag==2){
            if(arr[ind]>arr[ind-2]){
                return aa[ind][flag][flag1]= maxx(arr,ind+1,3,1)+1;
            }
            else{
                return aa[ind][flag][flag1]=0;
            }
        }else{
            if(arr[ind]>arr[ind-1]){
                return aa[ind][flag][flag1]= maxx(arr,ind+1,3,1)+1;
            }
            else{
                return aa[ind][flag][flag1]= 0;
            }
        }
    }

    public static void main(String[] args) {
        Scanner scanner=new Scanner(System.in);
        int n=scanner.nextInt();
        aa=new int[n][4][2];
        for(int j=0;j<n;j++){
            for(int i=0;i<4;i++){
                for(int k=0;k<2;k++){
                    aa[j][i][k]=-1;
                }
            }
        }
        int[] arr=new int[n];
        for(int i=0;i<n;i++){
            arr[i]=scanner.nextInt();
        }
        System.out.println(maxx(arr,0,0,0));

    }


}
