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.BufferedReader;
import java.io.BufferedWriter;
import java.io.FileWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.*;
import static java.lang.Math.*;

public class RemoveOneElement {

	static BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
	static BufferedWriter writer = new BufferedWriter(new OutputStreamWriter(System.out));

	static int n;
	static int[] a;
	
	static void process() throws Exception {
		int[] rt = new int[n], lt = new int[n];
		Arrays.fill(rt,  1);
		Arrays.fill(lt,  1);
		
		int ans = 1;
		
		for (int i = 1; i < n; i++) {
			if (a[i] > a[i - 1]) {
				lt[i] = lt[i - 1] + 1;
			}
			ans = max(ans, lt[i]);
		}
		
		for (int i = n-2; i >= 0; i--) {
			if (a[i + 1] > a[i]) {
				rt[i] = rt[i + 1] + 1;
			}
			ans = max(ans, rt[i]);
		}
		
		for (int i = 0; i < n - 2; i++) {
			if (a[i + 2] > a[i]) {
				ans = max(ans, lt[i] + rt[i + 2]);
			}
		}
		
		writer.write(String.format("%d", ans));
		writer.newLine();
	}

	public static void main(String[] args) throws Exception {
		//		writer = new BufferedWriter(new FileWriter("output.txt"));
		String data[], input;
		n = Integer.parseInt(reader.readLine());
		a = Arrays.asList(reader.readLine().split(" ")).stream().mapToInt(Integer::parseInt).toArray();
		process();
		writer.close();
	}

}
