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(" ")))
listas = [[a[0]]]
j = 0
for i in range(0, len(a)-1):
    if a[i+1] > a[i]:
        listas[j].append(a[i+1])
    else:
        j += 1
        listas.append([])
        listas[j].append(a[i+1])
long = []

for i in range(0, len(listas)):
    long.append(len(listas[i]))

for i in range(0, len(listas)-1):
    if listas[i][len(listas[i])-2] < listas[i+1][0]:
        long.append(len(listas[i]) + len(listas[i+1]) - 1)
    elif len(listas[i+1]) >= 2 and listas[i][len(listas[i])-1] < listas[i+1][1]:
        long.append(len(listas[i]) + len(listas[i+1]) - 1)


print(max(long))
