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 Main{
	
	static int mod=1000000007;
	public static void main(String[] args) throws IOException {
		Writer out=new Writer(System.out);
		Reader in=new Reader(System.in);
		int t=1;
		
		while(t-->0) {		
				
			int n=in.nextInt();
			int a[]=in.readArray(n);
			int l[]=array(n,1);
			int r[]=array(n,1);
			for(int i=1; i<n; i++) 	if(a[i]>a[i-1]) l[i]=l[i-1]+1;
			for(int i=n-2; i>=0; i--) if(a[i]<a[i+1]) r[i]=r[i+1]+1;
			int ans=findMax(l);
			for(int i=1; i<n-1; i++) {
				int temp=Integer.MIN_VALUE;
				if(a[i-1]<a[i+1]) temp=l[i-1]+r[i+1];
				ans=Math.max(temp, ans);
			}
			out.println(ans);
			
		}
		out.close();		
	}
		
/*********************************** UTILITY CODE BELOW **************************************/	
	
	static void sort(int[] a) {
		ArrayList<Integer> list=new ArrayList<>();
		for (int i:a) list.add(i);
		Collections.sort(list);
		for (int i=0; i<a.length; i++) a[i]=list.get(i);
	}
	
	static int [] array(int n, int value) {
		
		int a[]=new int[n];
		for(int i=0; i<n; i++) a[i]=value;
		return a;
		
	}
	
	static int findMax(int [] a) {
		int max=Integer.MIN_VALUE;
		for(int i: a) if(i>max) max=i;
		return max;
	}
	
	static class Reader{
		
		BufferedReader br;
		StringTokenizer to;
		
		Reader(InputStream stream){
			br=new BufferedReader(new InputStreamReader(stream));
			to=new StringTokenizer("");
		}
		
		String next() {
			while(!to.hasMoreTokens()) {
				try {
					to=new StringTokenizer(br.readLine());	
				}catch(IOException e) {}
				
			}
			return to.nextToken();
			
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		
		long nextLong() {
			return Long.parseLong(next());
		}
		
		int [] readArray(int n) {
			int a[]=new int[n];
			for(int i=0; i<n ;i++) a[i]=nextInt();
			return a;
		}
		long [] readLongArray(int n) {
			long a[]=new long[n];
			for(int i=0; i<n ;i++) a[i]=nextLong();
			return a;
		}
		
	}
	
	static class Writer extends PrintWriter{
		Writer(OutputStream stream){
			super(stream);
		}
		void println(int [] array) {
			for(int i=0; i<array.length; i++) {
				print(array[i]+" ");
			}
			println();
		}
		void println(long [] array) {
			for(int i=0; i<array.length; i++) {
				print(array[i]+" ");
			}
			println();
		}
	}
	
}