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.
def Remove_One_Element(array):
    regroup=[]
    for i,item in enumerate(array):
        if i!=0 and item>regroup[-1][-1]:
            regroup[-1].append(item)
        else:
            regroup.append([item])
    
    ans=0
    for i,item in enumerate(regroup):
        ## base case: itself
        ans=max(ans,len(item))
        if i<len(regroup)-1:
            ## remove the last of current:
            if len(item)>1 and item[-2]<regroup[i+1][0]:
                ans=max(ans,len(item)+len(regroup[i+1])-1)
            ## remove the first of next
            if len(regroup[i+1])>1 and item[-1]<regroup[i+1][1]:
                ans=max(ans,len(item)+len(regroup[i+1])-1)
        ## remove single bad point
        if i<len(regroup)-2:
            if len(regroup[i+1])==1 and item[-1]<regroup[i+2][0]:
                ans=max(ans,len(item)+len(regroup[i+2]))
    return ans
                
            



if __name__=="__main__":
  input_len=int(raw_input().strip())
  array=map(int,raw_input().split(" "))
  print Remove_One_Element(array)

