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().strip())
A = list(map(int, input().strip().split()))
 
max_l = 0
fir_sub_max_l = 0
sec_sub_max_l = 1
last = A[0]
sec_last = -1000000000000000000000000000000000
remove_type = 'other'
for i, a in enumerate(A[1:]):
    if a > last:
        sec_sub_max_l += 1
        sec_last = last
        last = a
    else:
        if a > sec_last or (i != n-2 and A[i+2] > last):
            max_l = max(max_l, fir_sub_max_l+sec_sub_max_l)
            fir_sub_max_l = sec_sub_max_l - 1
            sec_sub_max_l = 1
            sec_last = last
            last = a
        else:
            max_l = max(max_l, fir_sub_max_l+sec_sub_max_l)
            fir_sub_max_l = 0
            sec_sub_max_l = 1
            sec_last = last
            last = a
max_l = max(max_l, fir_sub_max_l+sec_sub_max_l)
print(max_l)
