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.Scanner;

/**
 *
 * @author Parsa
 */
public class Main {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int n = input.nextInt();
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = input.nextInt();
        }
        int maxWithRemove = 0;
        int cYR = 1;
        int fromLastGap = 1;

        for (int i = 0; i < arr.length - 1; i++) {
            if (arr[i] < arr[i + 1]) {
                cYR++;
                fromLastGap++;
                maxWithRemove = Math.max(maxWithRemove, cYR);
            } else {
                if (i + 2 < arr.length) {
                    //arr[i+1] < arr[i]
                    if (arr[i + 2] > arr[i]) {
                        maxWithRemove = Math.max(maxWithRemove, cYR);
                        cYR = fromLastGap + 1;
                        fromLastGap = 1;
                        i = i + 1;
                    } else if (arr[i + 2] > arr[i + 1]) {
                        if(i-1 >= 0) {
                        if (arr[i + 1] > arr[i - 1]) {
                            maxWithRemove = Math.max(maxWithRemove, cYR);
                            cYR = fromLastGap + 1;
                            fromLastGap = 2;
                            i = i + 1;
                        } else {
                            maxWithRemove = Math.max(maxWithRemove, cYR);
                            cYR = 1;
                            fromLastGap = 1;
                            i = i;
                        }
                        } else {
                          cYR = 1;
                          fromLastGap = 1;  
                        }
                    } else {
                        maxWithRemove = Math.max(maxWithRemove, cYR);
                        cYR = 1;
                        fromLastGap = 1;
                        i = i + 1;
                    }
                } else {
                    maxWithRemove = Math.max(maxWithRemove, cYR);
                    i = n; //break
                }

            }

        }
        maxWithRemove = Math.max(maxWithRemove, cYR);
        if(n == 0) 
            System.out.println("0");
        else
        System.out.println(maxWithRemove);
    }

}