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.

import sys


class Input():
    stdin_input = []

    def get_next_token(self):
        if not self.stdin_input or len(self.stdin_input) == 0:
            self.stdin_input = sys.stdin.readline().split(' ')
        result = self.stdin_input[0]
        self.stdin_input = self.stdin_input[1:]
        return result

    def get_next_line(self):
        return sys.stdin.readline()

    def read_str(self):
        return self.get_next_token()

    def read_int(self):
        return int(self.get_next_token())

read = Input()
size = read.read_int()
left = [1]*size
right = [1]*size
stdin_input = sys.stdin.readline().split(' ')
t = list(map(lambda a: int(a), stdin_input))
res = 1
for i in range(1, size):
    if t[i-1] < t[i]:
        left[i] = left[i-1] + 1

for i in range(size-2, -1, -1):
    if t[i] < t[i+1]:
        right[i] = right[i+1] + 1

for i in range(0, size-2):
    if t[i] < t[i+2]:
        res = max(res, left[i] + right[i+2])

for i in range(0, size-1):
    if t[i] < t[i+1]:
        res = max(res, left[i] + right[i+1])

print(res)
