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())
s = input()
l = list(map(int, s.split()))
records = []
current = 1
for i in range(1, len(l)):
    if l[i - 1] < l[i]:
        current += 1
    if l[i - 1] >= l[i]:
        records.append(current)
        append0 = False
        if i > 1 and l[i] <= l[i-2]:
            append0 = True
        if i < len(l) - 1 and l[i-1] < l[i+1]:
            append0 = False
        if append0:
            records.append(0)
        current = 1
records.append(current)

mx = records[0]
for i in range(1, len(records)):
    mx = max(mx, records[i] + records[i-1] - 1, records[i])

print(mx)




