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 D1272 {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int N = in.nextInt();
        int[] A = new int[N];
        for (int n=0; n<N; n++) {
            A[n] = in.nextInt();
        }
        int max = 1;
        for (int i=0; i<2; i++) {
            int gap = -1;
            int start = 0;
            int idx = 1;
            int last = A[0];
            while (idx < N) {
                if (A[idx] > last) {
                    max = Math.max(max, idx-start+1-(gap == -1 ? 0 : 1));
                    last = A[idx];
                } else if (gap == -1) {
                    gap = idx;
                } else {
                    last = A[gap];
                    idx = gap;
                    start = gap;
                    gap = -1;
                }
                idx++;
            }
            int[] B = new int[N];
            for (int n=0; n<N; n++) {
                B[n] = -A[N-1-n];
            }
            A = B;
        }
        System.out.println(max);
    }

}
