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())
a = list(map(int, input().split()))
arr = [0] * n
arr[0] = 1
temp = [-1] * n
m = 1
for i in range(1, n):
	if a[i] > a[i - 1]:
		arr[i] += arr[i - 1] + 1
		m = max(m, arr[i])
	else:
		arr[i] = 1
if arr[n - 1] == 1:
	temp[n - 1] = n - 1
for i in range(n - 2, -1, -1):
	if arr[i] == 1:
		temp[i] = i
	else:
		temp[i] = temp[i + 1]
if m == n:
	print(m)
else:
	for i in range(1, n - 1):
		if a[i - 1] < a[i + 1]:
			p = n - 1
			if i + 2 < n:
				if temp[i + 2] != -1:
					p = temp[i + 2] - 1
			m = max(m, arr[i - 1] + (arr[p] - arr[i + 1] + 1))
	print(m)