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.
import math
import random

def type1(): return map(int, input().split())


def type2(): return list(type1())


def type3(): return int(input())






n=type3()
a=type2()

forward=[1]*n
for i in range(1,n):
    if a[i]>a[i-1]:
        forward[i]=forward[i-1]+1
   
backward=[1]*n
for i in range(n-2,-1,-1):
    if a[i]<a[i+1]:
        backward[i]=backward[i+1]+1
# print(forward,backward)
maxi=max(max(forward),max(backward))
for i in range(1,n-1):
    if a[i-1]<a[i+1]:
        maxi=max(maxi,forward[i-1]+backward[i+1]) 

print(maxi)  

# print(length,rng)
# ans=-1
# l=len(length)
# if l>=2:
#     for i in range(l):
#         dup=length[i]
#         dup1=length[i]
#         if i==0:
#             if rng[i+1][0]-rng[i][1]==2 and a[rng[i+1][0]]>a[rng[i][1]]:
#                 dup1+=length[i+1]
#         elif i==l-1:
#             if rng[i][0]-rng[i-1][1]==2 and  a[rng[i][0]]>a[rng[i-1][1]]:
#                 dup+=length[i-1]
#         else:
#             if rng[i][0]-rng[i-1][1]==2 and a[rng[i][0]]>a[rng[i-1][1]]:
#                 dup+=length[i-1]
#             if rng[i+1][0]-rng[i][1]==2 and a[rng[i+1][0]]>a[rng[i][1]]:
#                 dup1+=length[i+1]
        
#         ans=max(ans,dup1,dup)
#     print(ans)
# else:
#     print(length[0])