D. Remove One Elementtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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 \dots r] = a_l, a_{l + 1}, \dots, a_r. The subarray a[l \dots r] is called strictly increasing if a_l < a_{l+1} < \dots < a_r.InputThe first line of the input contains one integer n (2 \le n \le 2 \cdot 10^5) — the number of elements in a.The second line of the input contains n integers a_1, a_2, \dots, a_n (1 \le a_i \le 10^9), where a_i is the i-th element of a.OutputPrint one integer — the maximum possible length of the strictly increasing contiguous subarray of the array a after removing at most one element.ExamplesInput
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
NoteIn 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.
5
1 2 5 3 4

4 
['brute force', 'dp', '*1500']