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.
#!python3
"""
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"""

from collections import deque, Counter
import array
from itertools import combinations, permutations
from math import sqrt
import unittest


def read_int():
    return int(input().strip())


def read_int_array():
    return [int(i) for i in input().strip().split(' ')]

######################################################

n = read_int()
array = read_int_array()

count = 2 if array[0] < array[1] else 1
prevcount = 1
delcount = 0
maxcount = count
for i in range(2, n):
    if array[i-1] < array[i]:
        if delcount == 0 and array[i-2] < array[i]:
            delcount = prevcount + 1
        else:
            delcount += 1
        prevcount = count
        count += 1
    else:
        delcount = prevcount + 1 if array[i-2] < array[i] else 0
        prevcount = count
        count = 1

    maxcount = max(maxcount, count, delcount)

print(maxcount)

"""

1 2 5 3 4
    ^

1 2 


              v
0 1 2 3 4 5 6 7 8 9  10
6 5 5 6 7 1 8 9 1 10 11

i count prevcount maxcount
2 1 1 1
3 1 1 1
4 2 1 2
5 3 2 3
6 1 3 3
7 2 4 4


"""




