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.
/*
If you want to aim high, aim high
Don't let that studying and grades consume you
Just live life young
******************************
If I'm the sun, you're the moon
Because when I go up, you go down
*******************************
*/
import java.util.*;
import java.io.*;

   public class x1272D
   {
      public static void main(String args[]) throws Exception
      {
         BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));  
         StringTokenizer st = new StringTokenizer(infile.readLine());
         int N = Integer.parseInt(st.nextToken());
         int[] arr = readArr(N, infile, st);
         //solve
         int[][] dp = new int[N][2];
         dp[0][0] = 1;
         dp[1][1] = 1;
         for(int i=1; i < N; i++)
         {
            if(arr[i-1] < arr[i])
            {
               dp[i][0] = Math.max(dp[i][0], dp[i-1][0]+1);
               dp[i][1] = Math.max(dp[i][1], dp[i-1][1]+1);
            }
            else
            {
               //don't skip
               dp[i][0] = Math.max(dp[i][0], 1);
               dp[i][1] = Math.max(dp[i][1], 1);
            }
            if(i >= 2 && arr[i-2] < arr[i])
               dp[i][1] = Math.max(dp[i][1], dp[i-2][0]+1);
         }
         //I am retarded
         int res = dp[0][0];
         for(int i=0; i < N; i++)
            for(int a=0; a < 2; a++)
               res = Math.max(res, dp[i][a]);
         System.out.println(res);
      }
      public static int[] readArr(int N, BufferedReader infile, StringTokenizer st) throws Exception
      {
         int[] arr = new int[N];
         st = new StringTokenizer(infile.readLine());
         for(int i=0; i < N; i++)
            arr[i] = Integer.parseInt(st.nextToken());
         return arr;
      }
   }