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.
def arr_inp():
    return [float(x) for x in stdin.readline().split()]


from sys import *
from collections import *

n, a, ans, mem, mem2 = int(input()), arr_inp(), 0, deque([]), deque([])
if n == 2:
    if a[0] < a[1]:
        exit(print(2))
    else:
        exit(print(1))

mi, ma, l = 0, 0, 0

for i in range(n):
    if a[i] > mi:
        l += 1
        mi = a[i]
    else:
        ans = max(ans, l)
        mi, l = a[i], 1
    mem.append(l)

ans = max(ans, l)

ma = mem[n - 1]
mem2.appendleft(ma)

for i in range(n - 2, -1, -1):
    if mem[i] < mem[i + 1]:
        mem2.appendleft(ma)
    else:
        ma = mem[i]
        mem2.appendleft(ma)

for i in range(1, n - 1):
    if a[i + 1] > a[i - 1] and (a[i] >= a[i + 1] or a[i] <= a[i - 1]):
        if mem2[i] == mem2[i - 1] or mem2[i] == mem2[i + 1]:
            ans = max(ans, mem2[i + 1] + mem2[i - 1] - 1)
        else:
            ans = max(ans, mem2[i + 1] + mem2[i - 1])

# print(mem, mem2)
print(ans)
