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 Main {
    public static void main(String args[]) {
        Scanner s = new Scanner(System.in);
        int n = s.nextInt();
        int arr[] = new int[n];
        for(int i = 0; i < n; i++){
            arr[i] = s.nextInt();
        }
        int left[] = new int[n];
        int right[] = new int[n];
        left[0] = 1;
        int ans = 1;
        for(int i = 1; i < n; i++){
            if(arr[i] > arr[i - 1]){
                left[i] = left[i - 1] + 1;
            }
            else{
                left[i] = 1;
            }
            ans = Math.max(ans,left[i]);
        }
        right[n - 1] = 1;
        for(int i = n - 2; i >= 0; i--){
            if(arr[i] < arr[i + 1]){
                right[i] = right[i + 1] + 1;
            }
            else{
                right[i] = 1;
            }
            ans = Math.max(ans,right[i]);
        }
        for(int i = 1; i < n - 1; i++){
            if(arr[i + 1] > arr[i - 1]){
                ans = Math.max(ans,left[i - 1] + right[i + 1]);
            }
        }
        System.out.println(ans);
        
    }
}