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 D
{
	public static void solve(FastIO io)
	{
		int n = io.nextInt();
		
		int[] a = new int[n];

		for (int i = 0; i < n; i++)
			a[i] = io.nextInt();

		int[][] dp = new int[n][2];
		dp[0][0] = dp[0][1] = 1;

		ArrayList<Integer> pts = new ArrayList<>();

		for (int i = 1; i < n; i++)
			if (a[i] > a[i-1])
			{
				dp[i][0] = dp[i-1][0] + 1;
				dp[i][1] = dp[i-1][1] + 1;
			}
			else
			{
				dp[i][0] = 1;

				if (i != 1 && a[i] > a[i-2])
					dp[i][1] = 1 + dp[i-2][0];
				else
					dp[i][1] = 1;
			}

		int[] fwd = new int[n];
		fwd[0] = 1;

		for (int i = 1; i < n; i++)
			if (a[i] > a[i-1])
			{
				fwd[i] = fwd[i-1] + 1;
			}
			else
			{
				fwd[i] = 1;
			}

		int[] bwd = new int[n];
		bwd[n-1] = 1;

			for (int i = n-2; i >= 0; i--)
				if (a[i] < a[i+1])
				{
					bwd[i] = bwd[i+1] + 1;
				}
				else
				{
					bwd[i] = 1;
				}

		
		int max = 1;

		for (int i = 0; i < n; i++)
		{
			max = Math.max(max, Math.max(fwd[i], bwd[i]));

			if (i != 0 && i != n-1 && a[i-1] < a[i+1])
				max = Math.max(max, fwd[i-1] + bwd[i+1]);
		}

		// io.println(Arrays.toString(fwd));
		// io.println(Arrays.toString(bwd));
		io.println(max);
	}

	public static void main(String[] args) {
		FastIO io = new FastIO();


		solve(io);
		


		io.close();
	}
}

class FastIO extends PrintWriter
{
	BufferedReader r = new BufferedReader(new InputStreamReader(System.in));
	StringTokenizer st = new StringTokenizer("");

	FastIO()
	{
		super(System.out);
	}

	public String next()
	{
		while (!st.hasMoreTokens())
		{
			try {
				st = new StringTokenizer(r.readLine());
			} catch (Exception e) {
				//TODO: handle exception
			}
		}
		return st.nextToken();
	}

	public int nextInt()
	{
		return Integer.parseInt(next());
	}

	public long nextLong()
	{
		return Long.parseLong(next());
	}

	public double nextDouble()
	{
		return Double.parseDouble(next());
	}
}
