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.
from collections import deque
from collections import OrderedDict
import math
 
import sys
import os
import threading
import bisect
 
import operator
 
import heapq
 
 
from atexit import register
from io import BytesIO
 
#sys.stdin = BytesIO(os.read(0, os.fstat(0).st_size))
#sys.stdout = BytesIO()
#register(lambda: os.write(1, sys.stdout.getvalue()))
 
 
import io
#input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
#sys.stdin = open("F:\PY\\test.txt", "r")
input = lambda: sys.stdin.readline().rstrip("\r\n")
#input = sys.stdin.readline
 


def fun1(i, k):
    if i<=k:
        return i
    else:
        return k-(i-k)

#solved by dp
        
    
    
n = int(input())
ar = [0]+list(map(int, input().split()))
dpI = [1]*(n+5)
dpU = [1]*(n+5)
answer = 1
for i in range(2,n+1):
    if ar[i-1]<ar[i]:
        dpI[i]+=dpI[i-1]
    answer = max(answer, dpI[i])
        
for i in range(n-1, 0, -1):
    if ar[i+1]>ar[i]:
        dpU[i]+=dpU[i+1]

for i in range(2, n):
    if ar[i-1]<ar[i+1]:
        temp = dpI[i-1]+dpU[i+1]
        #print(i-1, i+1, temp)
        answer = max(answer, temp)      
print(answer)

sys.exit(0)

def gcs(a, b):
    n = len(a)
    m = len(b)
    f = [[0]*(n+1) for i in range(m+1)]
    for i in range(1, n):
        for j in range(1, m):
            if a[i]==b[j]:
                f[i][j]=f[i-1][j-1]+1
            else:
                f[i][j]=max(f[i-1][j], f[i][j-1])
    i, j, l = n-1, m-1, 0
    answer = []
    while(i!=0):
        if f[i][j]==f[i-1][j]+1 and f[i][j]==f[i][j-1]+1:
            print(i, j, l)
            answer.append(a[i])
            i-=1
            l = j-1
        j-=1
        if j==0:    
            i-=1
            j=l 
        
    for i in range(0,n):
        for j in range(0,m):
            print(f[i][j], end=" ")
        print("\n", end="")
    print(answer)
    return f[n-1][m-1]

print(gcs('1baccbca', '2abcabaac'))
    

for t in range(int(input())):
    n =  int(input())
    ar1 = [' ']+list(map(str, input().split()))
    #ar1 = [' ']+ar1
    ar2 = [' ']+list(map(str, input().split()))
    dp = [[0]*(n+1) for i in range(n+1)]
 
    
    for i in range(1, n+1):
        for j in range(1, n+1):
            dp[i][j]=dp[i-1][j]
            if ar1[i]==ar2[j]:
                dp[i][j]=dp[i-1][j-1]+1
            else:
                dp[i][j]=max(dp[i][j-1], dp[i-1][j])
    
    





'''
sys.exit(0)
lV = [0]*10
lV[1]=1
for i in range(2, 10):
   if i<10:
       lV[i]=lV[i-1]+i
   else:
       lV[i]=lV[i-1]+1+i%10


#it's okey
def findOne(n, k):
    for i in range(1, 10):
        sumA=i
        sumA+=lV[min(i+k, 9)]-lV[i]
        sumA+=lV[max(i+k-9, 0)]
        print(sumA)
        if sumA==n:
            return i
    return 0

findOne(7,9)

for t in range(int(input())):
    n, k = map(int, input().split())
    oneS = findOne(n,k)
    if oneS!=0:
        print(oneS)
        continue
    n-=lV[k]
    if n<0:
        print(-1)
        continue
    print(lV)
    
   ''' 