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
import sys
from collections import defaultdict,Counter,deque,OrderedDict
import bisect
#sys.setrecursionlimit(1000000)
input = iter(sys.stdin.buffer.read().decode().splitlines()).__next__
ilele = lambda: map(int,input().split())
alele = lambda: list(map(int, input().split()))
def list2d(a, b, c): return [[c] * b for i in range(a)]
#def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
#INF = 10 ** 18
#MOD = 1000000000 + 7
from itertools import accumulate,groupby

def groupSequence(lst):
    res = [[lst[0]]]
    for i in range(1,len(lst)):
        if lst[i-1] < lst[i]:
            res[-1].append(lst[i])
        else:
            res.append([lst[i]])
    return res

N = int(input())
A = alele()
B = groupSequence(A)
#print(B)
Ans = len(B[0])
for i in range(1,len(B)):
    x = len(B[i])
    Ans = max(Ans,x)
    if len(B[i-1]) > 1 and B[i-1][-2] < B[i][0]:
        Ans = max(Ans,len(B[i-1]) + x - 1)
    if x>1 and B[i][1] > B[i-1][-1]:
        Ans = max(Ans,len(B[i-1]) + x - 1)
print(Ans)
