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=[int(x) for x in input().split()]
a=[]
b=[]
j=0
last=0
for i in l:
    if j<i:
        a.append(last+1)
        last+=1
    else:
        a.append(1)
        last=1
    j=i
j=10**10
last=0
for i in range(n-1,-1,-1):
    if l[i]<j:
        b.append(last+1)
        last+=1
    else:
        b.append(1)
        last=1
    j=l[i]
b=b[::-1]
end=a
start=b
m=max(max(end),max(start))
for i in range(1,n-1):
    if l[i-1]<l[i+1]:
        m=max(m,end[i-1]+start[i+1])
print(m)