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 {

    static int[][] a;

    public static void main(String[] args) throws IOException {
//        br = new BufferedReader(new FileReader(new File("cutting.in")));
//        out = new PrintWriter(new File("cutting.out"));
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        int PUTEN = 1;
        for (int POMOGI = 0; POMOGI < PUTEN; POMOGI++) {
            int n = nextInt();
            int[] a = new int[n];
            int[] dpr = new int[n];
            int[] dpl = new int[n];
            int ans = 1;
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            Arrays.fill(dpl, 1);
            Arrays.fill(dpr, 1);
            for (int i = n - 2; i >= 0; i--) {
                if (a[i + 1] > a[i]) dpr[i] = dpr[i + 1] + 1;
                ans = Math.max(ans, dpr[i]);
            }
            for (int i = 1; i < n; i++) {
                if (a[i - 1] < a[i]) dpl[i] = dpl[i - 1] + 1;
                ans = Math.max(dpl[i], ans);
            }
            for (int i = 0; i < n - 2; i++) {
                if (a[i] < a[i + 2]) {
                    ans = Math.max(ans, dpl[i] + dpr[i + 2]);
                }
            }
            out.println(ans);
        }
        out.close();
    }


    static BufferedReader br;
    static PrintWriter out;
    static StringTokenizer in = new StringTokenizer("");

    static String next() throws IOException {
        while (!in.hasMoreTokens()) {
            in = new StringTokenizer(br.readLine());
        }
        return in.nextToken();
    }

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

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

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

    static int gcd(int a, int b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }
}