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 RemoveOneElement {
	public static void main(String[] args) {
		int maxLength=0;
		int currLength=1;
		Scanner scan = new Scanner(System.in);
		int[] arr = new int[scan.nextInt()+2];
		arr[0]=1000000009; arr[arr.length-1]=0;
		for(int count=1; count<arr.length-1; count++) {
			arr[count]=scan.nextInt();
		}
		
		int[] ascend = new int[arr.length];
		int[] descend = new int[arr.length];
		ascend[1]=1; descend[descend.length-2]=1;
		
		for(int i=2; i<arr.length-1;i++) {
			if(arr[i]>arr[i-1]) {
				ascend[i]=ascend[i-1]+1;
			}
			else {
				ascend[i]=1;
			}
			maxLength=Math.max(maxLength, ascend[i]);
		}
		
		for(int i=descend.length-2;i>0;i--) {
			if(arr[i]<arr[i+1]) {
				descend[i]=1+descend[i+1];
			}
			else {
				descend[i]=1;
			}
		}
		
		for(int i=1; i< arr.length-1; i++) {
			if(arr[i-1]<arr[i+1] && (ascend[i-1]+descend[i+1]>maxLength)) {
				maxLength = ascend[i-1]+descend[i+1];
			}
		}
		
		scan.close();
		System.out.println(maxLength);
	}
	
	private static int bruteForce() {
		int maxLength=0;
		int currLength=1;
		Scanner scan = new Scanner(System.in);
		int[] arr = new int[scan.nextInt()];
		for(int count=0; count<arr.length; count++) {
			arr[count]=scan.nextInt();
		}
		for(int i = 0; i<arr.length; i++) {
			for(int j=0; j<arr.length;j++) {
				if(j!=i && j!=arr.length-1) {
					if((j+1!=i && arr[j] < arr[j+1]) || (j+1==i && j+2<arr.length && arr[j]<arr[j+2])) {
						currLength++;
					}
					else {
						if(currLength>maxLength) maxLength = currLength;
						currLength=1;
					}
				}
			}
			if(currLength>maxLength) maxLength = currLength;
			currLength=1;

		}
		
		for(int j=0; j<arr.length-1;j++) {
			if( arr[j] < arr[j+1]) {
				currLength++;
			}
			else {
				if(currLength>maxLength) maxLength = currLength;
				currLength=1;
			}
			
		}
		if(currLength>maxLength) maxLength = currLength;
		return maxLength;
	}
	
	
	
}
