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())
arr=list(map(int,input().split()))
ind=0
dp=[]
co = 0
maxi=1
for i in range(0,n-1):
    if arr[i]>=arr[i+1]:
        if ind==i:
            dp.append([ind])
            ind+=1
        else:
            if (len(dp)>0 and len(dp[-1])>1 )and (arr[dp[-1][1]-1]<arr[ind] or arr[dp[-1][1]]<arr[ind+1]):
                if maxi < dp[-1][1]-dp[-1][0]+i-ind+1:
                    maxi = dp[-1][1]-dp[-1][0]+i-ind+1
            else:
                if maxi < i-ind+1:
                    maxi = i-ind+1
            dp.append([ind,i])
            ind=i+1
i=n-1
if ind==n-1:
    dp.append([ind])
    ind+=1
else:
    if (len(dp)>0 and len(dp[-1])>1 )and (arr[dp[-1][1]-1]<arr[ind] or arr[dp[-1][1]]<arr[ind+1]):
        if maxi < dp[-1][1]-dp[-1][0]+i-ind+1:
            maxi = dp[-1][1]-dp[-1][0]+i-ind+1
    else:
        if maxi< i-ind+1:
            maxi = i-ind+1
    dp.append([ind,n-1])
print(maxi)
    