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 copy import copy


def arr_float_inp():
    return [float(s) for s in input().split()]


def arr_int_inp():
    return [int(s) for s in input().split()]


def int_inp():
    return int(input())


def float_inp():
    return float(input())


def comp(a):
    return a[0]


if __name__ == '__main__':
    n = int_inp()
    a = arr_int_inp()

    F = [1] * n
    for i in range(1, n):
        if a[i] > a[i - 1]:
            F[i] = F[i - 1] + 1

    F_new = [1] * n
    F_new[-1] = F[-1]
    for i in range(n - 1, 0, -1):
        if a[i - 1] < a[i]:
            F_new[i - 1] = F_new[i]
        else:
            F_new[i - 1] = F[i - 1]

    ans = max(F)
    for i in range(0, n - 2):
        if a[i + 2] > a[i]:
            ans = max(ans, F[i] + F_new[i + 2] - F[i + 2] + 1)

    print(ans)
