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.util.Scanner;

public class Q5_MireBala {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int[] input = new int[n];
        for (int i = 0; i < n; i++) input[i] = scanner.nextInt();
        int[] dpfw = dpFinderFW(input);
        int[] dpbw = dpFinderBW(input);
        int[] results = new int[n];
        int result=1;
        for (int i = 1; i < n; i++) {
            results[i] = dpfw[i];
            if ((i < n - 1) && (input[i + 1] > input[i - 1])) {
                if ((dpbw[i + 1] + dpfw[i - 1]) > dpfw[i]) {
                    results[i] = dpbw[i + 1] + dpfw[i - 1];
                }
            }
            if(results[i]>result) result = results[i];
        }
        System.out.println(result);
    }

    static int[] dpFinderFW(int[] input) {
        int[] dp = new int[input.length];
        int result = 1;
        dp[0] = 1;
        for (int i = 1 ; i < input.length; i ++) {
            if (input[i] > input[i - 1]) dp[i] = dp[i - 1] + 1;
            else dp[i] = 1;
            if (dp[i] > result) result = dp[i];
        }
        return dp;
    }
    static int[] dpFinderBW(int[] input) {
        int[] dp = new int[input.length];
        int result = 1;
        dp[input.length-1] = 1;
        for (int i = input.length-2; -1 < i; i--) {
            if (input[i] < input[i +1]) dp[i] = dp[i +1] + 1;
            else dp[i] = 1;
            if (dp[i] > result) result = dp[i];
        }
        return dp;
    }
}