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()]
c,b,x,d = 1,0,0,0
e,f,g,y = 0,0,0,0
for i in range(1,n):
	if a[i-1] < a[i]:
		c = c+1
	else :
		x =  max(x,b+c-d)
		if a[i-2] >= a[i]:
			b,d = 0,0
		else: 
			d,b = 1,c
		c = 1
i = 0
x =  max(x,b+c-d)
for i in range(0,n-1):
	if a[i] < a[i+1]:
		e = e + 1
	else :
		y = max(y,e+f+1-g)
		if i+2 >= n :
			e,f,g = -1,-1,1
		else:
			if a[i] < a[i+2] :
				g = 1
				f = e + 1
			else :
				g = 0
				f = 0
		e = 0
y = max(y,e+f+1-g)	
print(max(x,y))		
