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.
from sys import stdin, stdout
outputs = []
n = int(stdin.readline().strip())
arr = [int(num) for num in stdin.readline().strip().split()]
req = []
l, r = 0, 0
for i in range(n-1):
    if arr[i] < arr[i+1]:
        r += 1
    else:
        req.append([l, r])
        l = i+1
        r = i+1
if l == n-1:
    req.append([n-1, n-1])
else:
    req.append([l, r])
res = 1
for i in range(len(req)):
    res = max(res, (req[i][1]-req[i][0])+1)
prev1, next1 = None, None
prev2, next2 = None, None
tot1, tot2 = 0, 0
for i in range(len(req)):
    prev1, next1 = req[i][0]-1, req[i][0]+1
    prev2, next2 = req[i][1]-1, req[i][1]+1
    tot1, tot2 = 0, 0
    if prev1 == -1 or next1 == n:
        pass
    else:
        if arr[prev1] < arr[next1]:
            tot1 += req[i-1][1]-req[i-1][0]+1
            if next1 > req[i][1]:
                tot1 += req[i+1][1]-req[i+1][0]+1
            else:
                tot1 += req[i][1]-req[i][0]
            res = max(res, tot1)
        else:
            pass
    if prev2 == -1 or next2 == n:
        pass
    else:
        if arr[prev2] < arr[next2]:
            tot2 += req[i+1][1] - req[i+1][0] + 1
            if prev2 < req[i][0]:
                tot2 += req[i-1][1] - req[i-1][0] + 1
            else:
                tot2 += req[i][1] - req[i][0]
            res = max(res, tot2)
        else:
            pass
print(res)






