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 = list(map(int, input().split())) + [0]
max_len = 0
lr = []
cnt = left = right = 0
for i in range(n-1):
    if a[i] < a[i+1]:
        right += 1
    else:
        lr.append([left, right])
        left = right = i + 1
lr.append([left, right])
for i in range(len(lr) - 1):
    if lr[i][1] - lr[i][0] + 1 > max_len:
        max_len = lr[i][1] - lr[i][0] + 1
    if a[lr[i][1]] < a[lr[i+1][0] + 1] or a[lr[i][1] - 1] < a[lr[i+1][0]]:
        ls = lr[i+1][1] - lr[i][0]
        if ls > max_len:
            max_len = ls
if lr[-1][1] - lr[-1][0] + 1 > max_len:
    max_len = lr[-1][1] - lr[-1][0] + 1

print(max_len)
