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) throws IOException {
        BufferedReader inp = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));

        int size = Integer.parseInt(inp.readLine());
        int[] given = new int[size];
        String[] s1 = inp.readLine().split(" ");
        int[] dpleft = new int[size];
        int[] dpright = new int[size];
        int[] dp1 = new int[size];
        for(int i=0;i<size;i++){
            given[i] = Integer.parseInt(s1[i]);
            dpleft[i] = 1;
            dpright[i] = 1;
            dp1[i] = 1;
        }

        for(int i=1;i<size;i++){
            if(given[i-1]<given[i]){
                dpleft[i] = dpleft[i-1] + 1;
            }

            if(given[size-1-i]<given[size-i]){
                dpright[size-1-i] = dpright[size-i]+1;
            }
        }


        int max = 1;
        for(int i=1;i<size;i++){

            max = Math.max(dpleft[i],max);

            if(i>1){
                if(given[i-2]<given[i]) {
                    max = Math.max(dpleft[i-2]+dpright[i],max);
                }
            }
        }

//        print(dp);
//        print(dp1);
        System.out.println(max);





    }
    static void print(int[] a){
        for(int i=0;i<a.length;i++){
            System.out.print(a[i]+" ");
        }
        System.out.println();
    }
}
