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.io.*;
import java.util.*;

public class Q4 {


    public static void main(String[] args) {


        InputReader in = new InputReader();
        PrintWriter out = new PrintWriter(System.out);

        int N = in.nextInt();
        int arr[]=new int [N+1];
        for (int i = 0; i < N; i++)
            arr[i]=in.nextInt();

        int front[]=new int [N+1],end[]=new int [N+1];
        Arrays.fill(front,1);
        Arrays.fill(end,1);

        for(int i =1;i<N;i++){
            if(arr[i]>arr[i-1])
                front[i]+=front[i-1];
        }
        front[N]=end[N]=0;
        for(int i =N-2;i>=0;i--){
            if(arr[i]<arr[i+1])
                end[i]+=end[i+1];
        }

        long ans =0,temp=0;
        for(int i =0;i<N;i++){
            ans=Math.max(ans,front[i]);

            temp=0;
            if(i==0)
                temp=end[i+1];
            else if(arr[i+1]>arr[i-1]){
                temp+=end[i+1]+front[i-1];
            }
            ans=Math.max(ans,temp);
        }

        out.println(ans);
        out.close();

    }

// Lunch  tym question cards wala


//    public static void main(String[] args) {
//
//        InputReader in = new InputReader();
//        PrintWriter out = new PrintWriter(System.out);
//
//        int q = in.nextInt();
//
//        while (q-- > 0) {
//
//            int  N=in.nextInt(),K=in.nextInt();
//            long arr[][]=new long [N][2];
//
//            for(int  i=0;i<N;i++)
//                arr[i][0]=in.nextInt();
//
//           long sum=0; // total num of cards
//
//            for(int  i=0;i<N;i++) {
//                arr[i][1] = in.nextInt();
//                sum+=arr[i][1];
//            }
//
//            Arrays.sort(arr,new Comparator<long[]>(){
//                public  int compare(long a[],long b[]){
//                    return Integer.compare((int)a[0],(int )b[0]);
//                }
//            });
//
//
//            long start=0,end=sum,total =sum,ans=0;
//            for(int i=0;i<K;i++){
//
//                int round=in.nextInt();
//
//                if(i%2==0){
//                    start+=total - round;
//                }else{
//                    end  = start+round;
//                    total= end -start;
//                }
//            }
//
//            long sl=0;
//            int pos=0;
//            for(int i=0;i<N;i++){
//                sl+=arr[i][1];
//                if(sl<start)
//                    arr[i][1]=0;
//                else{
//                    arr[i][1]=sl - start;
//                    pos=i;
//                    break;
//                }
//            }
//
//            end=end-start;
//            sl=0;
//
//            for(;pos <N;pos++){
//                sl+=arr[pos][1];
//                if(sl<=end)
//                   ans+=arr[pos][0]*arr[pos][1];
//                else {
//                    ans+=arr[pos][0]*(sl-end);
//                    break;
//                }
//            }
//
//            out.println(ans);
//
//        }
//
//
//        out.close();
//
//
//    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public long[] shuffle(long[] arr) {
            Random r = new Random();
            for (int i = 1, j; i < arr.length; i++) {
                j = r.nextInt(i);
                arr[i] = arr[i] ^ arr[j];
                arr[j] = arr[i] ^ arr[j];
                arr[i] = arr[i] ^ arr[j];
            }
            return arr;
        }

        public InputReader() {
            reader = new BufferedReader(new InputStreamReader(System.in), 32768);
            tokenizer = null;
        }

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(System.in), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public char nextChar() {
            return next().charAt(0);
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }


    }

}








