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()))
res = []
temp = [l[0]]
for j in range(1,n+1):
    if(j!=n and l[j]>l[j-1]):
        temp.append(l[j])
    else:
        res.append(temp)
        temp = [l[j]] if(j!=n) else 0
max_length = 0
for j in range(len(res)):
    max_length = max(max_length,len(res[j]))
for j in range(1,len(res)):
    if((len(res[j-1])>1 and res[j][0]>res[j-1][-2]) or (len(res[j])>1 and res[j][1]>res[j-1][-1])):
        max_length = max(max_length,len(res[j])+len(res[j-1])-1)
print(max_length)
        
        
    