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.ArrayList;
import java.util.Comparator;
import java.util.List;
import java.util.StringTokenizer;

public class RemoveOneElement { // Template for CF
    public static class ListComparator implements Comparator<List<Integer>> {

        @Override
        public int compare(List<Integer> l1, List<Integer> l2) {
            for (int i = 0; i < l1.size(); ++i) {
                if (l1.get(i).compareTo(l2.get(i)) != 0) {
                    return l1.get(i).compareTo(l2.get(i));
                }
            }
            return 0;
        }
    }

    public static void main(String[] args) throws IOException {
        // Check for int overflow!!!!
        // Should you use a long to store the sum or smthn?
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        int N = Integer.parseInt(f.readLine());
        StringTokenizer st = new StringTokenizer(f.readLine());
        List<Integer> list = new ArrayList<>();
        for (int i = 0; i < N; i++) {
            int a = Integer.parseInt(st.nextToken());
            list.add(a);
        }
        int[] right = new int[N];
        int[] left = new int[N];
        left[0] = 1;
        for (int i = 1; i < N; i++) {
            if (list.get(i) > list.get(i - 1)) {
                left[i] = left[i - 1] + 1;
            } else {
                left[i] = 1;
            }
        }
        right[N - 1] = 1;
        for (int i = N - 2; i >= 0; i--) {
            if (list.get(i) < list.get(i + 1)) {
                right[i] = right[i + 1] + 1;
            } else {
                right[i] = 1;
            }
        }
        int max = 0;
        for (int i = 0; i < left.length; i++) {
            max = Math.max(left[i], max);
        }
        for (int i = 1; i < N - 1; i++) {
            if (list.get(i - 1) < list.get(i + 1)) {
                int a = left[i - 1] + right[i + 1];
                max = Math.max(a, max);
            }
        }
        out.println(max);
        out.close();
    }

}