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;

public class CR605D {

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[n];
        int[] left = new int[n];
        int[] right = new int[n];
        left[0] = 1;
        right[n-1] = 1;

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

        int jackpot = -1;

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

        int max  = 0;

        for(int i=0; i<n; i++) {
            max = Math.max(max, left[i]);
        }

        for(int i=1; i<n-1; i++) {
            if(a[i-1] < a[i+1])
                max = Math.max(max, left[i-1] + right[i+1]);
        }

        System.out.println(max);

    }
}
