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 max_length(length, arr):
    sub_arr_1 = [1] * length
    sub_arr_2 = [1] * length
    for j in range(length-2, -1, -1):
        if arr[j] < arr[j+1]:
            sub_arr_1[j] = sub_arr_1[j+1] + 1
            sub_arr_2[j] = sub_arr_2[j+1] + 1
        if j+2 < length and arr[j] < arr[j+2]:
            sub_arr_2[j] = max(sub_arr_2[j], sub_arr_1[j+2] + 1)
    max_1 = max(sub_arr_1)
    max_2 = max(sub_arr_2)
    return max(max_1, max_2)


n = int(input(""))
second_line = input("")
a = second_line.split()
for i in range(0, n):
    a[i] = int(a[i])
print(max_length(n, a))

 	   			 						  	 	   	   	 	