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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class removeOneElement {
    static BufferedReader b = new BufferedReader(new InputStreamReader(System.in));
    static PrintWriter p = new PrintWriter(System.out);

    public static void main(String arg[]) throws IOException {
        int n = Integer.parseInt(b.readLine());
        StringTokenizer st = new StringTokenizer(b.readLine());
        int max = 0;
        int[] num = new int[n];
        int[] left = new int[n];
        int[] right = new int[n];
        for(int x = 0; x < n; x++){
            num[x] = Integer.parseInt(st.nextToken());
            if(x == 0){
                left[x] = 1;
            } else {
                if(num[x] > num[x - 1]){
                    left[x] = left[x - 1] + 1;
                } else {
                    left[x] = 1;
                }
            }
        }
        right[n - 1] = 1;
        for(int x = n - 2; x >= 0; x--){
            if(left[x] < left[x + 1]){
                right[x] = right[x + 1] + 1;
            } else {
                right[x] = 1;
            }
        }
        for(int x = 0; x < n; x++){
            int k;
            if(x == 0){
                k = right(right, x);
                if(num[0] < num[1]){
                    k++;
                }
            } else if(x == n - 1){
                k = left(left, x);
                if(num[x] > num[x - 1]){
                    k++;
                }
            } else {
                k = left(left, x);
                if(num[x - 1] < num[x + 1]){
                    k += right(right, x);
                }
            }
            if(max < k){
                max = k;
            }
        }
        p.println(max);
        p.close();
    }
    public static int left(int[] weight, int index){
        return weight[index - 1];
    }
    public static int right(int[] num, int index){
        return num[index + 1];
    }
}
