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.io.*;
import java.util.*;
public class Main {
    public static void main(String args[])
    {
        FastReader input=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
        int T=1;
        while(T-->0)
        {
            int n=input.nextInt();
            int a[]=new int[n];
            for(int i=0;i<n;i++)
            {
                a[i]=input.nextInt();
            }
            ArrayList<ArrayList<Integer>> l=new ArrayList<>();
            ArrayList<Integer> l1=new ArrayList<>();
            l1.add(0);
            for(int i=1;i<n;i++)
            {
                if(a[i]<=a[i-1])
                {
                    l1.add(i-1);
                    l.add(l1);
                    l1=new ArrayList<>();
                    l1.add(i);
                }
            }
            l1.add(n-1);
            l.add(l1);
            int max=Integer.MIN_VALUE;
            for(int i=0;i<l.size()-1;i++)
            {
                if(l.get(i).get(0)==l.get(i).get(1))
                {
                    max=Math.max(max,l.get(i+1).get(1)-l.get(i+1).get(0)+1);
                }
                else
                {
                    if(a[l.get(i).get(1)-1]<a[l.get(i+1).get(0)])
                    {
                        max=Math.max(max,l.get(i).get(1)-l.get(i).get(0)+l.get(i+1).get(1)-l.get(i+1).get(0)+1);
                    }
                }
                if(l.get(i+1).get(0)==l.get(i+1).get(1))
                {
                    max=Math.max(max,l.get(i).get(1)-l.get(i).get(0)+1);
                }
                else
                {
                    if(l.get(i+1).get(0)+1<n && a[l.get(i).get(1)]<a[l.get(i+1).get(0)+1])
                    {
                        max=Math.max(max,l.get(i).get(1)-l.get(i).get(0)+l.get(i+1).get(1)-l.get(i+1).get(0)+1);
                    }
                }
            }
            for(int i=0;i<l.size();i++)
            {
                max=Math.max(max,l.get(i).get(1)-l.get(i).get(0)+1);
            }
            out.println(max);
        }
        out.close();
    }
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}