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.
n = int(input())
a = list(map(int, input().split()))
inc_seq = []
last = 0
for i in range(len(a)):
    if i == 0 or a[i] > a[i - 1]:
        continue
    else:
        inc_seq.append((last, i - 1, a[i - 1]))
        last = i
inc_seq.append((last, len(a)-1, a[-1]))
maxList = list(map(lambda x: x[1] - x[0] + 1, inc_seq))
i = 0
j = 1
while j < len(inc_seq):
    try:
        if (inc_seq[i][1] + 1 == inc_seq[j][0]) and (a[inc_seq[i][1] - 1]< a[inc_seq[j][0]]):
            maxList.append(inc_seq[j][1] - inc_seq[i][0])
        elif (inc_seq[i][1] + 1 == inc_seq[j][0]) and (a[inc_seq[i][1]]< a[inc_seq[j][0] + 1]):
            maxList.append(inc_seq[j][1] - inc_seq[i][0])
    except:
        pass
    i += 1
    j += 1
print(max(maxList))
