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 {
    public static final boolean DO_LOG = false; // TODO: move to run params
    private static Logger log = new Logger();

    static class Task {

        PrintWriter out;
        MyScanner in;

        public void solve(MyScanner in, PrintWriter out) {
            this.in = in;
            this.out = out;

            // *_*

            int n = in.nextInt();
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = in.nextInt();
            }

            int[] f = new int[n];
            int[] g = new int[n];
            g[0] = 1;
            f[n - 1] = 1;
            for (int i = n - 2; i >= 0; i--) {
                f[i] = 1;
                if (a[i] < a[i + 1]) {
                    f[i] += f[i + 1];
                }
            }
            for (int i = 1; i < n; i++) {
                g[i] = 1;
                if (a[i] > a[i - 1]) {
                    g[i] += g[i - 1];
                }
            }
            log.info("F = " + Arrays.toString(f));
            log.info("G = " + Arrays.toString(g));

            int best = -1;
            for (int i = 0; i < n; i++) {
                best = Math.max(best, g[i] + f[i] - 1);
                if ((i < n - 2) && a[i] < a[i + 2]) {
                    best = Math.max(best, g[i] + f[i + 2]);
                }
            }
            out.println(best);

        }

    }

    public static void main(String[] args) {

        MyScanner in = new MyScanner();
        PrintWriter out = new PrintWriter(System.out);
        Task solver = new Task();

        solver.solve(in, out);

        out.close();
    }

    public static class Logger {

        public void info(String s) {
            if (DO_LOG) {
                System.out.println(s);
            }
        }
    }

    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            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;
        }
    }
}

/*me after this round
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 */