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 main(String[] args) {
		FastScanner sc = new FastScanner();
		int n = sc.nextInt();
		int[] arr = new int[n];
		for(int i = 0; i < n; i++) {
			arr[i] = sc.nextInt();
		}
		int[] L = new int[n];
		Arrays.fill(L, 1);
		for(int i = 1; i < n; i++) {
			if(arr[i] > arr[i-1]) L[i] += L[i-1];
		}
		int[] R = new int[n];
		Arrays.fill(R, 1);
		for(int i = n-2; i >= 0; i--) {
			if(arr[i] < arr[i+1]) R[i] += R[i+1];
		}
		int max = 0;
		for(int i = 0; i < n; i++) {
			max = Integer.max(L[i], max);
		}
		for(int i = 1; i < n-1; i++) {
			if(arr[i-1] < arr[i+1]) {
				max = Integer.max(L[i-1] + R[i+1], max);
			}
		}
		System.out.println(max);
	}
	static int min(int[] arr) {
		int res = Integer.MAX_VALUE;
		for(int k: arr) res = Integer.min(k, res);
		return res;
	}
	static class FastScanner {
		public BufferedReader reader;
		public StringTokenizer tokenizer;
		public FastScanner() {
			reader = new BufferedReader(new InputStreamReader(System.in), 32768);
			tokenizer = null;
		}
		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
		public double nextDouble() {
			return Double.parseDouble(next());
		}
		public String nextLine() {
			try {
				return reader.readLine();
			} catch(IOException e) {
				throw new RuntimeException(e);
			}
		}
	}


}
