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.
import sys


def read_ints():
    return [int(x) for x in sys.stdin.readline().strip().split()]


def main():
    N = read_ints()[0]
    nums = read_ints()
    
    pref = [0] * N 
    suf = [0] * N

    pref[0] = 1
    ans = 1
    for ix in range(1, N):
        pref[ix] = 1 + (pref[ix - 1] if nums[ix] > nums[ix - 1] else 0)
        ans = max(ans, pref[ix])

    suf[N - 1] = 1
    for ix in range(N - 2, -1, -1):
        suf[ix] = 1 + (suf[ix + 1] if nums[ix] < nums[ix + 1] else 0)
    
    for to_delete in range(1, N - 1):
        if nums[to_delete - 1] < nums[to_delete + 1]:
            ans = max(pref[to_delete - 1] + suf[to_delete + 1], ans)
    print(ans)    


if __name__ == '__main__':
    main()

