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())
l = list(map(int, input().split()))
mass = []
p = [l[0]]
le = []
for i in range(1, n):
    if l[i] > l[i - 1]:
        p += [l[i]]
    else:
        mass += [p]
        le += [len(p)]
        p = [l[i]]
if len(p) > 0:
    le += [len(p)]
    mass += [p]
res = max(le)
for i2 in range(1, len(mass)):
    p = mass[i2]
    p2 = mass[i2 - 1]
    if le[i2] == 1 and i2 < len(mass) - 1:
        if mass[i2 + 1][0] > p2[-1]:
            res = max(res, len(mass[i2 + 1]) + len(p2))
        continue
    if le[i2 - 1] > 1 and le[i2] > 1:
        if p[1] > p2[-1]:
            res = max(res, le[i2] + le[i2 - 1] - 1)
        if p2[-2] < p[0]:
            res = max(res, le[i2] + le[i2 - 1] - 1)
print(res)
