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
from itertools import chain, permutations

def res(x):
	result = 1
	current = 1
	for i in range(1, len(x)):
		if x[i] > x[i - 1]:
			current = current + 1
			result = max(result, current)
		else: 
			result = max(result, current)
			current = 1
		if result < current:
			current = result
	return result

def check(x):
	best = res(x)
	for pos in range(len(x)):
		new = x[:pos] + x[pos+1:]
		best = max(best, res(new))
	return best


n = int(sys.stdin.readline())
a = list(map(int, sys.stdin.readline().split(' ')))

def solve(a, n):
	dp = [[1 for i in range(2)] for j in range(n)]


	dp[0][0] = 1
	dp[0][1] = 1

	for i in range(1, n):
		if a[i] > a[i - 1]:
			dp[i][0] = dp[i-1][0] + 1
			dp[i][1] = dp[i-1][1] + 1
		if i > 1 and a[i] > a[i-2]:
			dp[i][1] = max(dp[i][1], dp[i - 2][0] + 1)

	return (max(chain(*dp)))

# permutations = list(permutations(range(7)))
# for p in permutations:
# 	a = solve(p, len(p))
# 	b = check(p)
# 	#print(p)
# 	if a != b:
# 		print('error')

print(solve(a, n))