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.
from typing import List


def first_calculation(array: List[int]):
    dp: List[int] = [1] * len(array)
    par: List[int] = [i for i in range(0, len(array))]

    for i in range(1, len(array)):
        if array[i] > array[i - 1]:
            dp[i] = dp[i - 1] + 1
            par[i] = par[i - 1]
        else:
            for j in range(par[i - 1], i):
                par[j] = i - 1

    for i in range(par[-1], len(array)):
        par[i] = len(array) - 1

    return dp, par


def with_removing(array: List[int], dp: List[int], par: List[int]):
    max_ret = 0
    for i in range(1, len(array)-1):

        if par[i+1] != par[i-1] and array[i+1] > array[i-1]:
            if array[i] > array[i+1]:
                max_ret = max(max_ret, dp[i-1] + dp[par[i+1]])
            else:
                max_ret = max(max_ret, dp[i-1] + dp[par[i+1]]-1)
    return max_ret


def solution(array: List[int]):
    dp, par = first_calculation(array)
    removed_element = with_removing(array, dp, par)
    return max(max(dp), removed_element)

_ = int(input())
array = list(map(int, input().split()))
print(solution(array))
