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 min = Integer.MAX_VALUE;

    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        int n = nextInt();
        int a[] = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        int max = 1;
        int dp[][] = new int[n][2];
        dp[0][0] = 1;
        if (a[0] < a[1]) {
            dp[1][0] = 2;
            max = 2;
        } else dp[1][0] = 1;
        for (int i = 2; i < n; i++) {
            if (a[i] > a[i - 1]) {
                dp[i][0] = dp[i - 1][0] + 1;
                dp[i][1] = dp[i - 1][1] + 1;
                if (a[i - 2] < a[i]) dp[i][1] = Math.max(dp[i][1], dp[i - 2][0] + 1);
            } else {
                dp[i][0] = 1;
                if (a[i - 2] < a[i]) dp[i][1] = dp[i - 2][0] + 1;
                dp[i][1] = Math.max(dp[i][1], 1);
            }
            max = Math.max(Math.max(dp[i][0], dp[i][1]), max);
        }
        out.println(max);
        out.close();
    }


    static BufferedReader br;
    static StringTokenizer st = new StringTokenizer("");

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

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

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

class point {
    int l, r;

    public point(int l, int r) {
        this.l = l;
        this.r = r;
    }
}
