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

N = int(sys.stdin.readline())
a = list(map(int, sys.stdin.readline().split()))
list_check = [1]*N
list_check.append(0)
list_r = [1 for _ in range(N)]
for i in range(1, N):
    if a[i] > a[i-1]:
        list_check[i] += list_check[i-1]

list_check_r = list_check[:]
s, e = 0, 1
while s<=e and e<N:
    #print(s, e)
    if list_check[e] < list_check[e+1]:
        e+=1
    elif list_check[e] > list_check[e+1]:
        for i in range((e-s+1)//2):
            list_check_r[i+s] = list_check[e-i]
            list_check_r[e-i] = list_check[i+s]
        s = e+1
        e +=1
    else:
        #print(s, e)
        e+=1
        s+=1
res = 0
for i in range(N):
    res = max(res, list_check[i])
    if 0<i<N-1:
        if a[i-1] < a[i+1]:
            res = max(res, list_check[i-1]+list_check_r[i+1])
print(res)
#print(list_check)
#print(list_check_r)
