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, sys
from collections import defaultdict, Counter, deque

INF = float('inf')
MOD = int(1e9) + 7
MAX = int(2e5) + 1

def solve():
	n = int(input())
	arr = array()
	n = len(arr)

	inc = [1 for i in range(n)]
	dec = [1 for i in range(n)]
	ans = 1

	for i in range(1, n):
		if arr[i - 1] < arr[i]:
			inc[i] = inc[i - 1] + 1
			ans = max(ans, inc[i])
			
	for i in range(n - 2, -1, -1):
		if arr[i] < arr[i + 1]:
			dec[i] = dec[i + 1] + 1
			ans = max(ans, dec[i])

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

	print(ans)

def main():
	t = 1 
	# t = int(input())
	for _ in range(t):
		solve()
















def gcd(a, b):
	while b:
		a, b = b, a%b
	return a

def input():
	return sys.stdin.readline().rstrip('\n').strip()

def print(*args, sep=' ', end='\n'):
	first = True
	for arg in args:
		if not first:
			sys.stdout.write(sep)
		sys.stdout.write(str(arg))
		first = False 

	sys.stdout.write(end)

def vars():
	return map(int, input().split())
 
def array():
	return list(map(int, input().split()))

if __name__ == "__main__":
	main()
