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 sys,bisect
input = sys.stdin.readline

############ ---- USER DEFINED INPUT FUNCTIONS ---- ############
def inp():
    return(int(input().rstrip()))
def inlt():
    return(list(map(int,input().rstrip().split())))
def insr():
    s = input().rstrip()
    return(s[:len(s) - 1])
def invr():
    return(map(int,input().rstrip().split()))
################################################################
############ ---- THE ACTUAL CODE STARTS BELOW ---- ############

n = inp()
nums = inlt()
val = [0 for i in range(n)]
cnt = 1;val[0] = 1
for i in range(1,n):
    if nums[i - 1] >= nums[i]:
        for j in range(i - 1,i - cnt - 1,-1):
            val[j] = cnt
        cnt = 1
    else:
        
        cnt += 1
    val[i] = cnt

for j in range(n - 1,n - cnt - 1,-1):
            val[j] = cnt
    
ans = 0
for i in range(1,n - 1):
    if nums[i + 1] <= nums[i] and nums[i + 1] > nums[i - 1]:
        ans = max(ans,val[i] - 1 + val[i + 1])
    elif nums[i - 1] >= nums[i] and nums[i + 1] > nums[i - 1]:
        ans = max(ans,val[i] - 1 + val[i - 1])
print(max(ans,max(val)))
