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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class RemoveElemet
{
    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());
        }
    }

    public static void main(String[] args)
    {
        FastReader in = new FastReader();
        int n = in.nextInt();

        int A[] = new int[n];
        for (int i = 0; i < n; i++)
            A[i] = in.nextInt();

        int len[] = new int[n];
        len[0] = 1; int max = 1;

        for (int i = 1; i < n; i++)
        {
            if (A[i] > A[i-1])
            {
                len[i] = len[i-1] + 1;
                if (len[i] > max)
                    max = len[i];
            }
            else
            {
                len[i] = 1;
            }
        }

        int right[] = new int[n];

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

        for (int i = n - 2; i > 0; i--)
        {
            if (A[i + 1] - A[i - 1] > 0)
                max = Math.max(max, len[i - 1] + right[i + 1]);
        }

        /*
        for (int i = 0; i < n; i++)
        {
            System.out.print(len[i] + " ");
        }
        System.out.println();
        for (int i = 0; i < n; i++)
        {
            System.out.print(right[i] + " ");
        }
        */

        System.out.println(Math.max(max, right[0]));
    }
}
