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.io.*;
import java.util.*;

public class RemoveOneElement {
	public static void main(String[] args) throws IOException {
		BufferedReader input = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(input.readLine());
		StringTokenizer st = new StringTokenizer(input.readLine());
		
		int[] num = new int[n];
		for (int i = 0; i < n; i++) num[i] = Integer.parseInt(st.nextToken());
		
		ArrayList<IncreasingArray> arr = new ArrayList<IncreasingArray>();
		IncreasingArray temp = new IncreasingArray(1, 0, 0);
		int maxLength = -1;
		for (int i = 1; i < n; i++) {
			if (num[i] > num[i - 1]) temp.append();
			else {
				maxLength = Math.max(maxLength, temp.length);
				arr.add(temp);
				temp = new IncreasingArray(1, i, i);
			}
		}
		maxLength = Math.max(maxLength, temp.length);
		arr.add(temp);
		
		for (int i = 0; i < arr.size() - 1; i++) {
			if (arr.get(i).isAttachable(num, arr.get(i + 1))) {
				maxLength = Math.max(maxLength, arr.get(i).length + arr.get(i + 1).length - 1);
			}
		}
		
		System.out.println(maxLength);
	}
}

class IncreasingArray {
	int length;
	int leftInx;
	int rightInx;
	IncreasingArray (int length, int leftInx, int rightInx) {
		this.length = length;
		this.leftInx = leftInx;
		this.rightInx = rightInx;
	}
	
	void append () {
		this.length++;
		this.rightInx++;
	}
	
	boolean isAttachable(int[] num, IncreasingArray incArr) {
		if (this.length == 1) return false;
		if (incArr.length == 1) return false;
		
		if (num[this.rightInx - 1] < num[incArr.leftInx]) return true;
		if (num[this.rightInx] < num[incArr.leftInx + 1]) return true;
		
		return false;
	}
}
