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.
def fastio():
    import sys
    from io import StringIO 
    from atexit import register
    global input
    sys.stdin = StringIO(sys.stdin.read())
    input = lambda : sys.stdin.readline().rstrip('\r\n')
    sys.stdout = StringIO()
    register(lambda : sys.__stdout__.write(sys.stdout.getvalue()))
fastio()

INF = 10**20
MOD = 10**9 + 7
I = lambda:list(map(int,input().split()))
from collections import defaultdict as dd

n, = I()
a = I()

ans = 0
inc = [1] * n
dec = [1] * n
for i in range(n-2, -1, -1):
	if a[i] < a[i+1]:
		inc[i] = (1 + inc[i+1])
for i in range(1, n):
	if a[i] > a[i-1]:
		dec[i] = 1 + dec[i-1]

ans = max(dec)

for i in range(1, n-1):
	if a[i-1] < a[i+1]:
		ans = max(ans, dec[i-1] + inc[i+1])
# print(inc)
# print(dec)
print(ans)
