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.
//package cf605;

import java.io.*;
import java.util.*;

public class oneElement {
    static BufferedReader in;

    public static void solve() throws IOException {
        int n = nextInt();
        Integer[] arr = nextArray(n);

        int[] rg = new int[n];
        int[] lf = new int[n];
        Arrays.fill(rg,1);
        Arrays.fill(lf,1);

        int ans = 1;

        for (int i = 1; i < n; i++) {
            if(arr[i-1] < arr[i])
                lf[i] = lf[i-1]+1;

            ans = Math.max(ans,lf[i]);
        }


        for (int i = n-2; i >= 0; i--) {
            if(arr[i+1] > arr[i])
                rg[i] = rg[i+1]+1;

            ans = Math.max(ans,rg[i]);
        }

        for (int i = 0; i < n - 2; ++i) {
            if (arr[i] < arr[i + 2])
                ans = Math.max(ans, lf[i] + rg[i + 2]);
        }

        System.out.println(ans);



    }

    public static void main(String[] args) throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        solve();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(in.readLine().trim());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(in.readLine().trim());
    }

    static Integer[] nextArray(int n) throws IOException {
        StringTokenizer st = new StringTokenizer(in.readLine());
        Integer[] tmp = new Integer[n];
        for (int i = 0; i < tmp.length; i++) {
            tmp[i] = Integer.parseInt(st.nextToken());
        }

        return tmp;
    }

}

