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())
a=list(map(int,input().split()))
d=[]
for i in range(0,n-1):
    d.append(a[i+1]-a[i])

i=0
flag=0
j=0
t=[]
   
while(i<n-1):
   
    count=0
    while(i<n-1 and d[i]>0):
        i=i+1
        count=count+1
    
    t.append([i,count+1])
    if(i==n-1 and count+1==n):
        flag=1
    i=i+1
m=0

k=i
i=0

for i in range(0,len(t)-1):
    
    if(d[t[i][0]+1]>0 and (a[t[i][0]+1]>a[t[i][0]-1] or a[t[i][0]+2]>a[t[i][0]])):
        
        c=t[i][1]+t[i+1][1]-1
    else:
        
        c=t[i][1]
    if(c>m):
        m=c
    


'''if(i<len(t)-1 and t[i+1][1]>m):
    
    m=t[i+1][1]
if(i<len(t)-1 and j>t[i][0]):
    
    c=t[len(t)-1][1]+t[i][1]-1
    if(c>m):
        m=c'''
if(len(t)!=1):
    if(d[t[i][0]+1]>0 and (a[t[i][0]+1]>a[t[i][0]-1] or a[t[i][0]+2]>a[t[i][0]] )):
        
        c=t[i][1]+t[i+1][1]-1
    else:
        
        c=t[i][1]
        c2=t[i+1][1]
        c=max(c,c2)
    if(c>m):
        m=c
if(len(t)==1):
    if(k==n-1):
        m=n-1        
if(flag==0):
    print(m)
else:
    print(n)