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(raw_input())
a = list(map(int,raw_input().split()))

z = []
temp = []
for i in a:
	if(len(temp) == 0):
		temp.append(i)
	else:
		if(i > temp[-1]):
			temp.append(i)
		else:
			z.append(temp)
			temp = []
			temp.append(i)
z.append(temp)
m = 0

for i in z:
	m = max(m,len(i))

for i in range(len(z)-1):
	if(len(z[i+1]) == 1 or len(z[i]) == 1):
		continue
	if(z[i][-2] < z[i+1][0]):
		m = max(m,len(z[i]) + len(z[i+1]) - 1)
	if(z[i][-1] < z[i+1][1]):
		m = max(m,len(z[i]) + len(z[i+1]) - 1)
print m
