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())
l=list(map(int,input().split()))
sufinc=[1]*n
count=1
for i in range(n-2,-1,-1):
	if l[i]<l[i+1]:
		count+=1
		sufinc[i]=count
	else:
		count=1
		sufinc[i]=count
#print (sufinc)
preinc=[1]*n
count=1
for i in range(1,n):
	if l[i]>l[i-1]:
		count+=1
		preinc[i]=count
	else:
		count=1
		preinc[i]=count
#print (preinc)
ans=0
ans=max(sufinc[0],preinc[-1])
ans=max(sufinc[1],preinc[-2],ans)
for i in range(1,n-1):
	if l[i+1]>l[i-1]:
		if preinc[i-1]+sufinc[i+1]>ans:
			ans=preinc[i-1]+sufinc[i+1]
	else:
		ans = max(ans,preinc[i-1],sufinc[i+1])
# flag=0
# for i in range(1,n):
# 	if l[i]<=l[i-1]:
# 		flag=1
# 		break
# if flag==0:
# 	print (n)
# else:
# 	print (ans)
print (ans)