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.*;

public class Max_length_of_subarray_after_remove_1_element {
    public static int maxlength_afterremovingoneelement(int[] arr, int n)
    {

        int prev[] = new int[n] ;
        int post[] = new int[n] ;
        prev[0] = 1;
        post[n - 1] = 1;
        int l = 0;


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


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


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


        for (int i = 1; i <= n - 2; i++)
        {
            if (arr[i - 1] < arr[i + 1])
                ans = Math.max(prev[i - 1] +
                        post[i + 1], ans);
        }
        return ans;

    }
    public static void main(String[] args)
    {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int arr[] = new int[n];

        for(int i =0;i<n;i++)
            arr[i]=sc.nextInt();

        int result = maxlength_afterremovingoneelement(arr,n);
        System.out.println(result);
    }
}
