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 javax.swing.text.html.HTMLDocument;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.nio.Buffer;
import java.util.*;

public class Main {
    public static void main(String[] args){
        try {
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            int n=Integer.parseInt(br.readLine());
            String[] ss=br.readLine().split(" ");
            int[] arr=new int[n];
            int[] left=new int[n];
            int[] right=new int[n];
            for(int i=0;i<n;i++){
                arr[i]=Integer.parseInt(ss[i]);
            }

            int max=1;
            left[0]=1;
            for(int i=1;i<n;i++){
                if(arr[i]>arr[i-1]){
                    left[i]=left[i-1]+1;
                }else{
                    left[i]=1;
                }
                max=Math.max(max,left[i]);
            }
            right[n-1]=1;
            for(int i=n-2;i>=0;i--){
                if(arr[i]<arr[i+1]){
                    right[i]=right[i+1]+1;
                }else{
                    right[i]=1;
                }
                max=Math.max(max,right[i]);
            }
            for(int i=1;i<n-1;i++){
                //System.out.println(left[i]+" "+right[i]);
                int u,v;
                u=left[i-1];
                v=right[i+1];
                if(arr[i-1]<arr[i+1]){
                    max=Math.max(u+v,max);
                }
            }
            System.out.println(max);
        } catch (Exception e) {
            System.out.println("kkkk "+ e.getMessage());
        }
    }
    static int modInverse(int x,int m){
        return power(x,m-2,m);
    }
    static int power(int x, int y, int m)
    {
        if (y == 0)
            return 1;

        long p = power(x, y / 2, m) % m;
        p = (p * p) % m;

        return (int)((y%2==0)? p : (x*p)%m);
    }
    static void shuffle(int[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            int temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }
    static class quad{
        int a,b,c,d;
        public quad(int a,int b,int c,int d){
            this.a=a;
            this.b=b;
            this.c=c;
            this.d=d;
        }
    }
}