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(' ')))
lefts = []
leftsc = []
rights = []
rightsc = []
b = 0
for i in range(0, n - 1):
    if b == 0:
        if l[i] < l[i + 1]:
            b = 1
            lefts.append(l[i])
            leftsc.append(i)
        else:
            lefts.append(l[i])
            leftsc.append(i)
            rights.append(l[i])
            rightsc.append(i)
    if l[i] >= l[i + 1] and b == 1:
        b = 0
        rights.append(l[i])
        rightsc.append(i)
if l[n-2] < l[n - 1]:
    rights.append(l[n - 1])
    rightsc.append(n - 1)
else:
    lefts.append(l[n-1])
    leftsc.append(n-1)
    rights.append(l[n - 1])
    rightsc.append(n - 1)
maxl = 0

for i in range(len(lefts)):
    maxl = max(maxl, rightsc[i] - leftsc[i] + 1)

if len(lefts) == 1:
    print(rightsc[0] - leftsc[0] + 1)
    exit(0)
for i in range(len(lefts) - 1):
    if rights[i] >= lefts[i + 1]:
        if rightsc[i] - 1 >= 0:
            if l[rightsc[i] - 1] < lefts[i + 1]:
                if maxl < rightsc[i + 1] - leftsc[i]:
                    maxl = rightsc[i + 1] - leftsc[i]
        if rightsc[i] + 1 < n:
            if leftsc[i + 1] + 1 < n:
                if l[rightsc[i]] < l[leftsc[i + 1] + 1]:
                    if maxl < rightsc[i + 1] - leftsc[i]:
                        maxl = rightsc[i + 1] - leftsc[i]
print(maxl)