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.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;

public class Main {
	
	static int INF = (int)1e9;
	
	public static void main(String[] argv)throws IOException {
		
		StringBuilder sb = new StringBuilder();
		InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        
        int n  = in.nextInt();
        int[] arr = new int[n];
        
        for (int i=0; i<n; i++)
        	arr[i] = in.nextInt();
        int[] toright = new int[n];
        int[] toleft = new int[n];
        
        toright[0] = 1;
        for (int i=1; i<n; i++) {
        	if (arr[i] > arr[i-1]) 
        		toright[i] = toright[i-1]+1;
        	else
        		toright[i] = 1;
        }
        
        toleft[n-1] = 1;
        for (int i=n-2; i>=0; i--) {
        	if (arr[i] < arr[i+1]) 
        		toleft[i] = toleft[i+1]+1;
        	else
        		toleft[i] = 1;
        }
        
        int res = 0;
        for (int i=0; i<n; i++) {
        	res = Math.max(res, toright[i]);
        	if (i > 0 && i < n-1 && arr[i-1] < arr[i+1]) {
        		res = Math.max(toright[i-1] + toleft[i+1], res);
        	}
        }
        System.out.println(res);
	}
	
	
	static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 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());
        }

	}
}


