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 RemoveOneElement {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int n = Integer.parseInt(sc.nextLine());
        String[] input = sc.nextLine().split(" ");

        int maxLength = 0;

        int currentLength = 0;
        int numberOfRemovedElements = 0;
        for (int i = 0; i < input.length; i++) {

            if (i == input.length - 1){
                if(currentLength > 0){
                    currentLength++;
                    if(currentLength > maxLength){
                        maxLength = currentLength;
                    }
                }
                break;
            }
            int item = Integer.parseInt(input[i]);
            int nextItem = Integer.parseInt((input[i + 1]));
            int previousItem = i == 0 ? -1 : Integer.parseInt(input[i - 1]);
            int nextNextItem = i == input.length - 2 ? -1 : Integer.parseInt(input[i + 2]);

            if(item >= nextItem){
                if(currentLength > 0 && nextItem > previousItem && numberOfRemovedElements == 0){
                    numberOfRemovedElements = 1;
                    continue;
                }else if(currentLength > 0 && item < nextNextItem && numberOfRemovedElements == 0){
                    numberOfRemovedElements = 1;
                    continue;
                }else{
                    currentLength ++;
                    if(currentLength > maxLength){
                        maxLength = currentLength;
                    }
                    currentLength = 0;
                    numberOfRemovedElements = 0;
                    continue;
                }

            }

            currentLength++;
        }

        System.out.println(maxLength);
    }
}
