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 javax.swing.*;
import java.io.*;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner input = new Scanner(new BufferedInputStream(System.in));
        int T = input.nextInt();
        int[] nums = new int[T];
        int[] begin = new int[T];
        int[] end = new int[T];
        begin[0] = 1;
        end[T-1] = 1;
        int max = 0;
        for (int i = 0; i < T; i++)
            nums[i] = input.nextInt();
        for (int i = 1; i < T; i++) {
            if (nums[i] > nums[i - 1])
                begin[i] = begin[i - 1] + 1;
            else
                begin[i] = 1;
            if (begin[i]>max)
                max = begin[i];
        }
        for (int i = T - 2; i>=0; i--)
            if (nums[i+1]>nums[i])
                end[i] = end[i+1]+1;
            else
                end[i] = 1;
        for (int i = 1; i < T-1;i++)
            if (nums[i-1]<nums[i+1])
                if (max<(begin[i-1]+end[i+1])) {
                    max = begin[i-1] + end[i+1];
                }
        System.out.println(max);
    }
}