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.*;
import java.io.*;

public class Remove_One_Element {

	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

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

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

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

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}

	}

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		FastReader t = new FastReader();
		PrintWriter o = new PrintWriter(System.out);
		int n = t.nextInt();
		int[] a = new int[n];
		int[] dp1 = new int[n];
		int[] dp2 = new int[n];
		dp1[0] = 1;
		dp2[n - 1] = 1;
		int max = 1;

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

		for (int i = 1; i < n; ++i) {
			if (a[i] > a[i - 1])
				dp1[i] = dp1[i - 1] + 1;
			else
				dp1[i] = 1;

			max = Math.max(dp1[i], max);
		}

		for (int i = n - 2; i >= 0; --i) {
			if (a[i] < a[i + 1])
				dp2[i] = dp2[i + 1] + 1;
			else
				dp2[i] = 1;
		}

		for (int i = 0; i < n - 2; ++i)
			if (a[i] < a[i + 2])
				max = Math.max(max, dp1[i] + dp2[i + 2]);

		o.println(max);

		o.flush();
		o.close();
	}
}
