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.*;
import static java.lang.Integer.*;
public class main{
    public static void main(String[] args) throws IOException{
        BufferedReader in=new BufferedReader(new InputStreamReader(System.in));
        int n=parseInt(in.readLine());
        String ss[]=in.readLine().split(" ");
        int arr[]=new int[n];
        for(int i=0;i<n;i++){
            arr[i]=parseInt(ss[i]);
        }
        int pre[]=new int[n];
        pre[0]=1;
        int suff[]=new int[n];
        suff[n-1]=1;
        int maxi=Integer.MIN_VALUE;
        for(int i=1;i<n;i++){
            if(arr[i]>arr[i-1]){
                pre[i]=pre[i-1]+1;
                maxi=max(maxi,pre[i]);
            }
            else if(arr[i]<=arr[i-1]){
                pre[i]=1;
                maxi=max(maxi,pre[i]);
            }
            if(arr[n-1-i]<arr[n-i]){
                suff[n-1-i]=suff[n-i]+1;
            }
            else{
                suff[n-1-i]=1;
            }
        }
        //System.out.println("prefix array  "+Arrays.toString(pre));
        //System.out.println("suffix array  "+Arrays.toString(suff));
        if(n==2){
            if(arr[0]<arr[1]){
                System.out.println(2);
            }
            else{
                System.out.println(1);
            }
            return;
        }
        for(int i=0;i<(n-2);i++){
            if(arr[i]<arr[i+2])
                maxi=max(maxi,pre[i]+suff[i+2]);
        }
        System.out.println(maxi);
    }
}