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.*;

public class Main{
    private static class Node{
        int s;
        int e;
        public Node(int s, int e){
            this.s = s;
            this.e = e;
        }
    }
    public static void main(String[] args) {
        int n;
        Scanner scan = new Scanner(System.in);
        n = scan.nextInt();
        int[] a = new int[n];
        for(int i = 0; i < n; i ++){
            a[i] = scan.nextInt();
        }
        int s = 0;
        int e = 0;
        int res = 0;
        ArrayList<Node> list = new ArrayList<>();
        for(int i = 1; i < n; i ++){
            if(a[i] > a[e]){
                e ++;
            }else{
                Node node = new Node(s,e);
                list.add(node);
                res = Math.max(node.e - node.s + 1,res);
                s = i;
                e = i;
            }
        }
        Node node = new Node(s,e);
        list.add(node);
        res = Math.max(node.e - node.s + 1,res);
        for(int i = 1; i < list.size(); i ++){
            Node cur = list.get(i);
            Node last = list.get(i - 1);
            if(last.e == last.s && cur.e == cur.s) continue;
            if(last.e != last.s && a[cur.s] > a[last.e - 1]){
                res = Math.max(last.e - last.s + cur.e - cur.s + 1, res);
            }
            if(cur.e != cur.s && a[last.e] < a[cur.s + 1]){
                res = Math.max(last.e - last.s + 1 + cur.e - cur.s,res);
            }
        }
        System.out.println(res);
    }
}