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.ArrayList;
import java.util.Scanner;

public class TaskD {
	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int n = s.nextInt();
		
		int prev = s.nextInt();
		Part curr = new Part(prev);
		ArrayList<Part> parts = new ArrayList<Part>();
		int max = 0;
		
		for(int i=1;i<n;i++) {
			int c = s.nextInt();
			if(prev < c) {
				curr.add(c);
			} else {
				parts.add(curr);
				max = Math.max(curr.length, max);
				curr = new Part(c);
			}
			prev = c;
		}
		parts.add(curr);
		max = Math.max(curr.length, max);
		
		for(int i=0;i<parts.size()-1;i++) {
			Part a = parts.get(i);
			Part b = parts.get(i+1);
			
			//System.out.println(a);
			//System.out.println(b);
			
			if(a.length > 1 && a.pre < b.first) {
				max = Math.max(max, a.length-1 + b.length);
			}
			if(b.length > 1 && a.last < b.second) {
				max = Math.max(max, a.length + b.length-1);
			}
		}
		
		System.out.println(max);
	}
}

class Part {
	int length,first,last,pre,second;
	
	public Part(int ins) {
		length = 1;
		first = ins;
		last = ins;
	}
	
	public void add(int x) {
		length++;
		if(length == 2) {
			second = x;
		}
		pre = last;
		last = x;
	}
	
	@Override
	public String toString() {
		return "Part: pre " + pre + " | first " + first;
	}
}
