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 = [int(x) for x in input().split()]
l.append(0)
l.insert(0, 987654321)

m = []
idx = 0
max = 0

for x in range(1, n + 2):
    if l[x - 1] >= l[x]:
        m.append([idx, x - 1, x - 1 - idx + 1])

        if x - 1 - idx + 1 > max:
            max = x - 1 - idx + 1

        idx = x

m.append([n + 1, n + 1, 1])
nm = len(m)

for x in range(1, nm - 1):
    if m[x][2] == 1:
        if l[m[x - 1][1]] < l[m[x + 1][0]]:
            if m[x - 1][2] + m[x + 1][2] > max:
                max = m[x - 1][2] + m[x + 1][2]
    else:
        if l[m[x - 1][1]] < l[m[x][0] + 1]:
            if m[x - 1][2] + m[x][2] - 1 > max:
                max = m[x - 1][2] + m[x][2] - 1
        if l[m[x][1] - 1] < l[m[x + 1][0]]:
            if m[x][2] + m[x + 1][2] - 1 > max:
                max = m[x][2] + m[x + 1][2] - 1

print(max)