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())
arr = [int(j) for j in input().split()]
arr += [-10**18]
temp = []
count = [arr[0]]
for i in range(1, n+1):
	if arr[i] <= arr[i-1]:
		temp += [count]
		count = [arr[i]]
	else:
		count += [arr[i]]

ma = 0
for x in temp:
	if len(x) > ma:
		ma = len(x)

ans = []
for i in range(len(temp)-1):
	kk = 0
	if len(temp[i]) != 1 and len(temp[i+1]) != 1:
		if temp[i][-2] < temp[i+1][0]:
			kk = len(temp[i]) + len(temp[i+1]) - 1
		if temp[i][-1] < temp[i+1][1]:
			kk = len(temp[i]) + len(temp[i+1]) - 1

	elif len(temp[i]) != 1 and len(temp[i+1]) == 1:
		if i != len(temp)-2 and temp[i][-1] < temp[i+2][0]:
			kk = len(temp[i] + len(temp[i+2]))

	elif len(temp[i]) == 1 and len(temp[i+1]) != 1:
		if i >= 1 and temp[i-1][-1] < temp[i+1][0]:
			kk = len(temp[i-1]) + len(temp[i+1])

	else:
		if i >= 1 and temp[i-1][-1] < temp[i+1][0]:
			kk = len(temp[i-1]) + len(temp[i+1])
		if i != len(temp)-2 and temp[i][-1] < temp[i+2][0]:
			kk = max(len(temp[i] + len(temp[i+2])), kk)

	if kk != 0:
		ans += [kk]
if len(ans) == 0:
	ans = [-100]

print(max(max(ans), ma))

# count = 1
# i = 1
# while i != 