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.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class CF1272D_RemoveOneElement {
	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		public Scanner() {
			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;
		}

	}

	static void print(Object b) {
		System.out.print(b);
	}

	static void println(Object b) {
		System.out.println(b);
	}

	static void println() {
		System.out.println();
	}

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner scanner = new Scanner();
		int n = scanner.nextInt();
		int[] arr = new int[n];
		int[] left = new int[n];
		int[] right = new int[n];
		int ans = 1;
		for (int i = 0; i < n; i++) {
			arr[i] = scanner.nextInt();
			left[i] = 1;
			right[i] = 1;
		}

		for (int i = 1; i < n; i++) {
			if (arr[i - 1] < arr[i]) {
				left[i] = left[i - 1] + 1;
				ans = Math.max(ans, left[i]);
			}
		}
		for (int i = n - 2; i >= 0; i--) {
			if (arr[i] < arr[i + 1]) {
				right[i] = right[i + 1] + 1;
				ans = Math.max(ans, right[i]);
			}
		}

		for (int i = 0; i < n - 2; i++) {
			if (arr[i] < arr[i + 2]) {
				ans = Math.max(left[i] + right[i+2], ans);
			}
		}
		println(ans);
	}

}
