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.util.*;                                                         
import java.io.*;

public class remEle{
    
    public static void main(String[] args) throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine().trim());
        String[] in = br.readLine().split(" ");
        long[] arr = new long[n];
        long[] left = new long[n];
        Arrays.fill(left , 1);
        long[] right = new long[n];
        Arrays.fill(right , 1);
        for(int i=0;i<n;i++){
            arr[i] = Long.parseLong(in[i]);
        }
        long ans = 1;
        for(int i=1;i<n;i++){
            if(arr[i] > arr[i - 1]){
                left[i] = left[i - 1] + 1;
            }
            ans = Math.max(ans , left[i]);
        }
        for(int i= n-2;i>=0;i--){
            if(arr[i] < arr[i + 1]){
                right[i] = right[i + 1] + 1;
            }
        }
        for(int i=1;i<n-1;i++){
            if(arr[i - 1] < arr[i + 1]){
            ans = Math.max( ans , left[i - 1] + right[i + 1]);
            }
        }
        System.out.println(ans);
    }
}