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 D {

    public static void main(String[] args) throws Exception {
        // FileInputStream inputStream = new FileInputStream("input.txt");
        // FileOutputStream outputStream = new FileOutputStream("output.txt");

        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);

        Solver solver = new Solver(); 
        solver.solve(1, in, out);
        out.close();
    }

    static class Solver {

        
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int[] a = new int[n + 2];
            for (int i = 1 ; i <= n ; i++) {
                a[i] = in.nextInt();
            }
            a[0] = 0;
            a[n + 1] = Integer.MAX_VALUE;
            int[] d1 = new int[n + 2];
            d1[0] = 0;
            d1[n + 1] = 0;
            int result = 0;
            for (int i = 1 ; i <= n ; i++) {
                if (a[i] > a[i - 1]) {
                    d1[i] = d1[i - 1] + 1;
                    result = Math.max(result, d1[i]);
                } else {
                    d1[i] = 1;
                }
            }
            int[] d2 = new int[n + 2];
            d2[n + 1] = d2[0] = 0;
            for (int i = n ; i >= 1 ; i--) {
                if (a[i] < a[i + 1]) {
                    d2[i] = d2[i + 1] + 1;
                } else {
                    d2[i] = 1;
                }
            }
            for (int i = 1 ; i <= n ; i++) {
                if (a[i - 1] < a[i + 1]) {
                    result = Math.max(result, d1[i - 1] + d2[i + 1]);
                }
            }
            out.println(result);
        }
    }

    static class InputReader {

        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public float nextFloat() {
            return Float.parseFloat(next());
        }
    }
}
