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 collections import deque
n  = int(input())
arr = [10**9+1]+list(map(int, input().split(" ")))+[0]

last = [0, 0]
j = 0
maxi = 0
for i in range(n+1):
	if arr[i] >= arr[i+1]:
		# print("YES", j, i)
		if last and last[1] == j-1 and (arr[last[1]-1] < arr[j] or arr[last[1]] < arr[j+1]):
			# if i < n and  
			maxi = max(maxi, (i - last[0]))
			# print(maxi)
		else:
			maxi = max(maxi, i - j + 1)
		last = [j, i]
		j = i+1
	# print(last, i, arr[i])
maxi = max(maxi, last[1] - last[0] + 1)
print(maxi)#, i, j)

"""
8
1 5 3 6 3 4 5 6

"""