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.
# https://codeforces.com/problemset/problem/1272/D

from sys import stdin, exit
from typing import List, Tuple


stdin.readline()  # ignore len
seq = [int(v) for v in stdin.readline().rstrip().split()]
r_max_seq = [0] * len(seq)
r_max_seq[-1] = 1
l_max_seq = [0] * len(seq)
l_max_seq[0] = 1

for i in range(len(seq) - 1, 0, -1):
    if seq[i - 1] < seq[i]:
        r_max_seq[i - 1] = r_max_seq[i] + 1
    else:
        r_max_seq[i - 1] = 1

for i in range(1, len(seq)):
    if seq[i - 1] < seq[i]:
        l_max_seq[i] = l_max_seq[i - 1] + 1
    else:
        l_max_seq[i] = 1

max_inc = max(l_max_seq)
for i in range(1, len(seq) - 1):
    if seq[i - 1] < seq[i + 1]:
        max_inc = max(max_inc, l_max_seq[i - 1] + r_max_seq[i + 1])

print(max_inc)
