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.
// package endsem;
import java.util.*;
import java.lang.Math;
import java.io.*;
public class Cf_two {
	public static void main(String[] args) throws IOException{
		Reader.init(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n=Reader.nextInt();
		int[] a=new int[n];
		int[] l=new int[n];
		int[] r=new int[n];
		for (int i = 0; i < a.length; i++) {
			a[i]=Reader.nextInt();
			l[i]=1;
			r[i]=1;
		}
		int ans=1;
		for (int i = r.length-2; i >= 0; i--) {
			if(a[i]<a[i+1])r[i]=r[i+1]+1;
			ans=Math.max(ans,r[i]);
		}
		for (int i = 1; i < l.length; i++) {
			if(a[i]>a[i-1])l[i]=l[i-1]+1;
			ans=Math.max(ans, l[i]);
		}
		for (int i = 0; i < a.length-2; i++) {
			if(a[i]<a[i+2])ans=Math.max(ans,l[i]+r[i+2]);
		}
		out.println(ans);
		out.flush();
	}

}	
	
class Reader {

    static BufferedReader reader;

    static StringTokenizer tokenizer;



    /** call this method to initialize reader for InputStream */

    static void init(InputStream input) {

        reader = new BufferedReader(

                     new InputStreamReader(input) );

        tokenizer = new StringTokenizer("");

    }



    /** get next word */

    static String next() throws IOException {

        while ( ! tokenizer.hasMoreTokens() ) {

            //TODO add check for eof if necessary

            tokenizer = new StringTokenizer(

                   reader.readLine() );

        }

        return tokenizer.nextToken();

    }



    static int nextInt() throws IOException {

        return Integer.parseInt( next() );

    }

	

    static double nextDouble() throws IOException {

        return Double.parseDouble( next() );

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

	}
