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.InputStreamReader;
import java.util.StringTokenizer;

public class P1272D
{
	public static void main(String[] args)
	{
		FastScanner scan = new FastScanner();
		int n = scan.nextInt();
		int[] arr = new int[n];
		for (int i = 0; i < n; i++)
		arr[i] = scan.nextInt();
		int[][] dp = new int[2][n];
		dp[0][0] = 1;
		dp[1][0] = 0;
		for (int i = 1; i < n; i++)
		{
			if (arr[i] > arr[i-1])
			{
				dp[0][i] = dp[0][i-1]+1;
				dp[1][i] = dp[1][i-1]+1;
			}
			else
			{
				dp[0][i] = 1;
				dp[1][i] = 1;
			}
			if (i == 1)
				continue;
			if (arr[i] > arr[i-2])
				dp[1][i] = Math.max(dp[1][i], dp[0][i-2]+1);
			else
				dp[1][i] = Math.max(dp[1][i], 1);
		}
		int ans = 0;
		for (int i = 0; i < n; i++)
		{
			ans = Math.max(ans, dp[0][i]);
			ans = Math.max(ans, dp[1][i]);
		}
		System.out.println(ans);
	}
	static class FastScanner
	{
		BufferedReader br;
		StringTokenizer st;

		public FastScanner()
		{
			try
			{
				br = new BufferedReader(new InputStreamReader(System.in));
				st = new StringTokenizer(br.readLine());
			} catch (Exception e)
			{
				e.printStackTrace();
			}
		}

		public String next()
		{
			if (st.hasMoreTokens())
				return st.nextToken();
			try
			{
				st = new StringTokenizer(br.readLine());
			} catch (Exception e)
			{
				e.printStackTrace();
			}
			return st.nextToken();
		}

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

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

		public String nextLine()
		{
			String line = "";
			try
			{
				line = br.readLine();
			} catch (Exception e)
			{
				e.printStackTrace();
			}
			return line;
		}
	}
}
