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.
#Tardes de coding. Problem D: Remove One Element
import random
def main():
	n = int(input())
	a = [int(number) for number in input().split()]
	# n = 8
	# a = [random.randint(0,15) for i in range(8)]
	#array that keeps track of the increasingly subsequences inside the array
	seq = [1 for i in range(n)]
	max_seq = 1
	# print(a)

	#construct subsequences array
	for i in range(1, n):
		if a[i] > a[i-1]:
			seq[i] = seq[i-1] + 1
	index = n - 1
	while index > 0:
		last_disrupt = index-seq[index]
		if last_disrupt > 0 and a[last_disrupt] != a[index]:
			#we get rid of the first element of the second sequence
			if a[last_disrupt - 1] >= a[last_disrupt + 1] and last_disrupt < n-2:
				if a[last_disrupt] < a[last_disrupt + 2]:
					if seq[last_disrupt] + seq[index] - 1 > max_seq:
						max_seq = seq[last_disrupt] + seq[index] - 1
			#we get rid of the last element of the first sequence
			elif a[last_disrupt-1] < a[last_disrupt + 1]:
				if seq[last_disrupt - 1] + seq[index] > max_seq:
					max_seq = seq[last_disrupt-1] + seq[index]
		if seq[index] > max_seq:
			max_seq = seq[index]
		index = last_disrupt
		
	print(max_seq)

if __name__ == "__main__":
	main()