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.*;
import java.io.*;

public class Div3_605D {
	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw = new PrintWriter(System.out);
		StringTokenizer st;
		
		int n = sc.nextInt();
		int[] array = new int[n];
		for(int i = 0; i < n; i++)
			array[i] = sc.nextInt();
		
		boolean[] check = new boolean[n];
		int[] count = new int[n];
		
		
		check[0] = true;
		count[0] = 1;
		for(int i = 1; i < n; i++)
			if(array[i] > array[i - 1]) {
				check[i] = true;
				count[i] = count[i - 1] + 1;
			} else {
				count[i] = 1;
			}
		
		int max = 0;
		for(int i = n - 1; i >= 0; i--) {
			int curr = count[i];
			max = Math.max(max, curr);
			for(int j = 0; j < curr; j++) {
				count[i] = curr;
				i--;
			}
			i++;
		}
		
		for(int i = 1; i < n - 1; i++) {
			if(check[i] == true && check[i + 1] == true)
				continue;
			if(check[i] == false) {
				if(array[i + 1] > array[i - 1]) {
					int c = count[i - 1];
					if(array[i + 1] > array[i])
						c += count[i] - 1;
					else
						c += count[i + 1];
					max = Math.max(max, c);
				}
			} else {
				if(array[i + 1] > array[i - 1]) {
					max = Math.max(max, count[i] - 1 + count[i + 1]);
				}
			}
		}
		
		System.out.println(max);
	}
}
