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
input=lambda : stdin.readline().strip()
from math import ceil,sqrt,factorial,gcd
from collections import deque
n=int(input())
l=list(map(int,input().split()))
z=[[0]]
m=1
for i in range(1,n):
	if l[i]>l[i-1]:
		if i==n-1:
			z[-1].append(i)
		pass
	else:
		if i!=n-1:
			z[-1].append(i-1)
			z.append([i])
		else:
			z[-1].append(n-2)
			z.append([i,i])
for i in z:
	m=max(i[1]-i[0]+1,m)
# print(z)
for i in range(1,len(z)):
	x=z[i-1][1]
	# print(x)
	if l[x-1]<l[z[i][0]]:
		# print(z[i][1]-z[i-1][0])
		m=max(m,z[i][1]-z[i-1][0])
	if z[i][0]+1<n and l[x]<l[z[i][0]+1]:
		m=max(m,z[i][1]-z[i-1][0])
print(m)