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.
n = int(input())

line = input().split(" ")

A = []
for e in line:
	A.append(int(e))

ans = 1

left = [1] * n
right = [1] * n

for i in range(1, n):
	if A[i] > A[i - 1]:
		left[i] = 1 + left[i - 1]
	if A[n - 1 - i] < A[n - i]:
		right[n - 1 - i] = 1 + right[n - i]

ans = 1
for i in range(n):
	ans = max(ans, left[i])
	ans = max(ans, right[i])

	if i > 0 and i < n - 1 and A[i - 1] < A[i + 1]:
		ans = max(ans, left[i - 1] + right[i + 1])

	# print(i, ans)

# print(left)
# print(right)
print(ans)