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 AP_2 {
	public static int calc (int arrayLength, int [] arr) {
		int [] m1 = new int [arrayLength];
		m1[0] = 1;
		for (int i = 1; i < arrayLength; i++) {
			if (arr[i] > arr[i-1])
				m1[i] = m1[i-1] + 1;
			else 
				m1[i] = 1;
		}
		
		int [] m2 = new int [arrayLength];
		m2[arrayLength - 1] = 1;
		for (int i = arrayLength - 2; i >= 0; i--) {
			if (arr[i+1] > arr[i])
				m2[i] = m2[i+1] + 1;
			else 
				m2[i] = 1;
		}
		
		int maxLength = 0;
		int tempLength = 1;
		for (int i = 0; i < arrayLength-1; i++) {
			if (arr[i] < arr[i+1])
				tempLength++;
			else
				tempLength = 1;
			maxLength = Math.max(tempLength, maxLength);
		}
		
		for (int i = 1; i <= arrayLength-2; i++)  {  
            if (arr[i-1] < arr[i+1])  
            	maxLength = Math.max(m1[i-1] + m2[i+1], maxLength);  
        }  
		
        return maxLength;
	}
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int arrayLength = scan.nextInt();
		scan.nextLine();

		int [] arr = new int [arrayLength];
		for (int i = 0; i < arrayLength; i++) 
			arr [i] = scan.nextInt();
		
		System.out.println(calc(arrayLength, arr));
		
		scan.close();
	}

}
		    		  		  	 	 		 				 			