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=[int(x) for x in input().split()]
i=1
d=[]
maxi=0
while i<n:
	c=1
	j=i
	while i<n and a[i]>a[i-1]:
		i+=1
		c+=1
	
	d.append([c,j,i])
	i+=1	
	maxi=max(maxi,d[-1][0])

for i in range(len(d)-1):

	if a[d[i][2]-2]<a[d[i+1][1]-1] or (d[i+1][1]!=n and a[d[i][2]-1]<a[d[i+1][1]]):
		maxi=max(maxi,d[i][0]+d[i+1][0]-1)	
print(maxi)	
	