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


drop = input()

elements = input().split(' ')
# elements=[6, 5, 4, 3, 2, 4, 3,5]
ri = []
li = []
for i in range(len(elements)):
    ri.append(1)
    li.append(1)
max1 = 1
for i in range(1, len(elements)):
    if (int(elements[i]) > int(elements[i - 1])):
        li[i] = li[i - 1] + 1
        if li[i] > max1:
            max1 = li[i]
    if (int(elements[-i]) > int(elements[-i - 1])):
        ri[-i - 1] = ri[-i] + 1


for i in range(len(elements) - 2):
    if (int(elements[i]) < int(elements[i + 2])):
        if (li[i] + ri[i + 2] > max1):
            max1 = li[i] + ri[i + 2]

print(max1)
