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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = in.nextInt();
            }
            int[] up = new int[n];
            up[0] = 1;
            for (int i = 1; i < n; i++) {
                if (a[i] > a[i - 1]) {
                    up[i] = up[i - 1] + 1;
                } else {
                    up[i] = 1;
                }
            }

            int[] bot = new int[n];
            bot[n - 1] = 1;
            for (int i = n - 2; i >= 0; i--) {
                if (a[i] < a[i + 1]) {
                    bot[i] = bot[i + 1] + 1;
                } else {
                    bot[i] = 1;
                }
            }

            int max = Math.max(up[n - 1], Math.max(bot[0], Math.max(bot[1], up[n - 2])));
            for (int i = 0; i < n; i++) {
                max = Math.max(max, Math.max(bot[i], up[i]));
            }
            for (int i = 1; i < n - 1; i++) {
                if (a[i - 1] < a[i + 1]) {
                    max = Math.max(max, bot[i + 1] + up[i - 1]);
                } else {
                    max = Math.max(max, bot[i + 1]);
                    max = Math.max(max, up[i - 1]);
                }
            }
            out.println(max);
        }

    }

    static class InputReader {
        final InputStream is;
        final byte[] buffer = new byte[1024];
        int curCharIdx;
        int nChars;

        public InputReader(InputStream is) {
            this.is = is;
        }

        public int read() {
            if (curCharIdx >= nChars) {
                try {
                    curCharIdx = 0;
                    nChars = is.read(buffer);
                    if (nChars == -1) {
                        return -1;
                    }
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return buffer[curCharIdx++];
        }

        public int nextInt() {
            int sign = 1;
            int c = skipDelims();
            if (c == '-') {
                sign = -1;
                c = read();
                if (isDelim(c)) {
                    throw new RuntimeException("Incorrect format");
                }
            }
            int val = 0;
            while (c != -1 && !isDelim(c)) {
                if (!isDigit(c)) {
                    throw new RuntimeException("Incorrect format");
                }
                val = 10 * val + (c - '0');
                c = read();
            }
            return val * sign;
        }

        private final int skipDelims() {
            int c = read();
            while (isDelim(c)) {
                c = read();
            }
            return c;
        }

        private static boolean isDelim(final int c) {
            return c == ' ' ||
                   c == '\n' ||
                   c == '\t' ||
                   c == '\r' ||
                   c == '\f';
        }

        private static boolean isDigit(final int c) {
            return '0' <= c && c <= '9';
        }

    }
}

