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.*;
import java.util.*;

public class Main {
    private static InputReader in;
    private static PrintWriter out;

    public static void main(String[] args) {
        in = new InputReader();
        out = new PrintWriter(System.out);
        int t = 1;
//        t = in.nextInt();
        for (int i = 0; i < t; ++i) {
            solve();
        }
        out.close();
    }

    private static void solve() throws RuntimeException {
        int n = in.nextInt();
        int[] a = new int[n];
        int[] diff = new int[n];
        for (int i = 0; i < n; ++i) {
            a[i] = in.nextInt();
        }
        for (int i = 1; i < n; ++i) {
            if (a[i] <= a[i - 1]) ++diff[i];
            diff[i] += diff[i - 1];
        }
//        out.println(Arrays.toString(diff));
        int[] incr = new int[n];
        int[] decr = new int[n];
        for (int i = 0; i < n; ++i) {
            int low = i, high = n - 1;
            int at = i;
            while (low <= high) {
                int mid = (low + high) >> 1;
                if (diff[mid] == diff[i]) {
                    at = mid;
                    low = mid + 1;
                } else {
                    high = mid - 1;
                }
            }
            incr[i] = at - i + 1;
        }
        for (int i = 0; i < n; ++i) {
            int low = 0, high = i;
            int at = i;
            while (low <= high) {
                int mid = (low + high) >> 1;
                if (diff[mid] == diff[i]) {
                    at = mid;
                    high = mid - 1;
                } else {
                    low = mid + 1;
                }
            }
            decr[i] = i - at + 1;
        }
//        out.println(Arrays.toString(incr));
//        out.println(Arrays.toString(decr));
        int ans = 1;
        for (int i = 0; i < n; ++i) {
            if (i > 0 && i + 1 < n) {
                if (a[i - 1] < a[i + 1]) {
                    ans = Math.max(ans, incr[i + 1] + decr[i - 1]);
                }
            } else if (i == 0) {
                ans = Math.max(ans, incr[i]);
            } else {
                ans = Math.max(ans, decr[i]);
            }
            ans = Math.max(ans, incr[i]);
        }
        out.println(ans);
    }

    static class InputReader {
        BufferedReader br;
        StringTokenizer st;

        public InputReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}