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.
from sys import stdin
n = int(stdin.readline())
arr = [int(x) for x in stdin.readline().split()]

flag = True

for i in range(n-1):
	if not arr[i]<arr[i+1]:
		flag = False
		break

if flag:
	print(n)
	quit()

ans = 1
possible = []

prev,ptr = n-1,n-1

while ptr>0:
	while ptr>0 and arr[ptr-1]<arr[ptr]: ptr -= 1
	ans = max(ans,prev-ptr+1)
	possible.append([ptr,prev])
	while ptr>0 and not arr[ptr-1]<arr[ptr]: ptr -= 1
	prev = ptr

for i in range(len(possible)-1,0,-1):

	start1,end1,start2,end2 = possible[i][0],possible[i][1],possible[i-1][0],possible[i-1][1]

	if end1+2==start2:
		if arr[end1]<arr[start2]: ans = max(ans,end1-start1+1+end2-start2+1)

	elif end1+1==start2:
		if start1!=end1 and start2!=end2:
			if arr[end1-1]<arr[start2] or arr[end1]<arr[start2+1]:
				ans = max(ans,end1-start1+end2-start2+1)

# print(possible)
print(ans)