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 A {
    static FastReader f = new FastReader();

    public static void main(String[] args) {
        int n = f.nextInt();
        int[] arr = new int[n];
        for(int i=0;i<n;i++) {
            arr[i] = f.nextInt();
        }

        int[] pref = new int[n], suff = new int[n];
        pref[0] = 1;
        int ans = 1;
        for(int i=1;i<n;i++) {
            if(arr[i-1] < arr[i]) {
                pref[i] = pref[i-1] + 1;
                ans = Math.max(ans, pref[i]);
            } else {
                pref[i] = 1;
            }
        }

        suff[n-1] = 1;
        for(int i=n-2;i>=0;i--) {
            if(arr[i] < arr[i+1]) {
                suff[i] = suff[i+1] + 1;
            } else {
                suff[i] = 1;
            }
        }

        for(int i=1;i<n-1;i++) {
            if(arr[i-1] < arr[i+1]) {
                ans = Math.max(ans, pref[i-1] + suff[i+1] + (arr[i-1] < arr[i] && arr[i] < arr[i+1] ? 1 : 0));
            }
        }

        System.out.println(ans);
    }


    //fast input reader
    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;
        }
    }
}