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;
from math import log2,sqrt;
from bisect import bisect_left,bisect_right
import bisect;
import sys;
from sys import stdin,stdout
import os
sys.setrecursionlimit(pow(10,6))
import collections
from collections import defaultdict
from statistics import median
# input=stdin.readline
# print=stdout.write
inf = float("inf")
def fun(l,n):
    prefix=[0]*n
    for i in range(1,len(l)):
        if l[i]>l[i-1]:
            prefix[i]=prefix[i-1]+1
    return prefix
def rev_fun(l,n):
    suffix=[0]*n;
    for i in range(len(l)-1-1,0,-1):
        if l[i]<l[i+1]:
            suffix[i]=suffix[i+1]+1
    return suffix
def generate(l,prefix,suffix):
    ans=1
    for i in range(len(prefix)):
        if i==0:
            ans=max(ans,suffix[i+1]+1)
        elif i==n-1:
            ans=max(ans,prefix[i-1]+1)
        elif l[i-1]<l[i]<l[i+1]:
            ans=max(ans,prefix[i-1]+1+suffix[i+1]+1+1)
        elif l[i-1]<l[i+1]:
            ans = max(ans, prefix[i - 1] + 1 + suffix[i + 1] + 1)
        else:
            ans=max(ans,prefix[i-1]+1,suffix[i+1]+1)
    return ans;
n=int(input())
l=list(map(int,input().split()))
if n==1:
    print(1)
elif n==2:
    if l[0]<l[1]:
        print(2)
    else:
        print(1)
else:

    prefix=fun(l,n)
    suffix=rev_fun(l,n)
    ans=generate(l,prefix,suffix)

    print(ans)

