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())
a = input().split()
b = []
for i in a:
    b.append(int(i))
last = b[0]
section = [b[0]]
sections = []
for i in b[1::]:
    if i > last:
        section.append(i)
    else:
        sections.append(section)
        section = [i]
    last = i
sections.append(section)

ans = 0
for i in sections:
    ans = max(ans, len(i))
Last_section = sections[0]
for i in sections[1::]:
    if len(i) > 1 and len(Last_section) > 1:
        if Last_section[-2] < i[0] or Last_section[-1] < i[1]:
            ans = max(ans, len(i) + len(Last_section) - 1)
    Last_section = i
print(ans)
    
