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 java.util.*;import java.io.*;
public class Main
{
 
    public static void process()throws IOException
    {
        int n=ni(),arr[]=new int[n+1];
        for(int i=1;i<=n;i++) arr[i]=ni();
        int p[]=new int[n+1],s[]=new int[n+1];
 
        // for(int i=2;i<n;i++){
        //  if(arr[i]>arr[i-1])
        //      p[i+1]=p[i-1]+1;
        //  else
        //      p[i+1]=1;
        // }
        // for(int i=n-1;i>=1;i--){
        //  if(arr[i+1]>arr[i])
        //      s[i-1]=s[i]+1;
        //  else
        //      s[i]=1;
        // }
        int res=-1;
 
        p[1]=1;
        for(int i=2;i<=n;i++){
            if(arr[i]>arr[i-1])
                p[i]=p[i-1]+1;
            else
                p[i]=1;
        }
        s[n]=1;
        for(int i=n-1;i>=1;i--){
            if(arr[i+1]>arr[i])
                s[i]=s[i+1]+1;
            else
                s[i]=1;
        }
        // pn(Arrays.toString(p));
        // pn(Arrays.toString(s));
        for(int i=2;i<=n-1;i++){
            if(arr[i-1]<arr[i+1]){
                res=Math.max(res,p[i-1]+s[i+1]);
            }
        }
        for(int i=1;i<=n;i++)
            res=Math.max(res,p[i]);
        pn(res);
    }
 
    static FastReader sc=new FastReader();
    //static AnotherReader sc;
 
    public static void main(String[]args)throws IOException
    {
        //sc=new AnotherReader();
        int t=1;
        while(t-->0)
            process();
        System.out.flush();
        System.out.close();  
    }
 
    static boolean multipleTC=false;
    static void pn(Object o){System.out.println(o);}
    static void p(Object o){System.out.print(o);}
    static void pni(Object o){System.out.println(o);System.out.flush();}
    static int ni()throws IOException{return sc.nextInt();}
    static long nl()throws IOException{return sc.nextLong();}
    static double nd()throws IOException{return sc.nextDouble();}
    static String nln()throws IOException{return sc.nextLine();}
    static long gcd(long a, long b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int gcd(int a, int b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int bit(long n)throws IOException{return (n==0)?0:(1+bit(n&(n-1)));}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////
    static class FastReader{BufferedReader br;StringTokenizer st;public FastReader()
    {br=new BufferedReader(new InputStreamReader(System.in));}String next()
    {while(st==null||!st.hasMoreElements())
    {try{st=new StringTokenizer(br.readLine());}
    catch(IOException e){e.printStackTrace();}}
    return st.nextToken();}int nextInt()
    {return Integer.parseInt(next());}long nextLong()
    {return Long.parseLong(next());}double nextDouble()
    {return Double.parseDouble(next());}
    String nextLine(){String str="";try
    {str=br.readLine();}catch(IOException e)
    {e.printStackTrace();}return str;}}
 
    static class AnotherReader{BufferedReader br; StringTokenizer st;
    AnotherReader()throws FileNotFoundException{
    br = new BufferedReader(new FileReader("input.txt"));}
    String next()throws IOException{
    while (st == null || !st.hasMoreElements()) {try{
    st = new StringTokenizer(br.readLine());}
    catch (IOException  e){ e.printStackTrace(); }}
    return st.nextToken(); } int nextInt() throws IOException{
    return Integer.parseInt(next());}
    long nextLong() throws IOException
    {return Long.parseLong(next());}
    double nextDouble()throws IOException { return Double.parseDouble(next()); }
    String nextLine() throws IOException{ String str = ""; try{
    str = br.readLine();} catch (IOException e){
    e.printStackTrace();} return str;}}
/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
}